Name________________________________________________
Algebra I – Pd ____
Date_________________________
Real Numbers and Properties
1A
Real Numbers
Real numbers are divided into two types, rational numbers and irrational numbers
I.
Rational Numbers:
 Any number that can be expressed as the quotient of two integers. (fraction).
 Any number with a decimal that repeats or terminates.
 Subsets of Rational Numbers:
A. Integers: rational numbers that contain no fractions or decimals.
{…,-2, -1, 0, 1, 2, …}
B. Whole Numbers: all positive integers and the number 0.
{0, 1, 2, 3, … }
C. Natural Numbers (counting numbers): all positive integers (not 0).
{1, 2, 3, … }
II.
Irrational Numbers:
 Any number that cannot be expressed as a quotient of two integers (fraction).
 Any number with a decimal that is non-repeating and non-terminal (doesn’t repeat and
doesn’t end).
 Most common example is π.
Properties
1) Commutative Properties of Addition and Multiplication:
 The order in which you add or multiply does not matter.
a+b=b+a
and
a∙b=b∙a
2) Symmetric Property:
 If a + b = c, then c = a + b
 If , then
3) Reflexive Property:
 a+b=a+b
 Nothing changes
4) Associative Properties of Addition and Multiplication.
 The grouping of addition and multiplication does not matter. (Parenthesis)
5) Transitive Property:
 If a = b and b = c, then a = c.
 If, and, then
6) Distributive Property:
 a (b + c) = ab + ac
and
a(b – c) = ab – ac
7) Additive Identity:
 When zero is added to any number or variable, the sum is the number or variable.
 a+0=a
8) Multiplicative Identity:
 When any number or variable is multiplied by 1, the product is the number or variable.
 a∙1=a
9) Multiplicative Property of Zero:
 When any number or variable is multiplied by zero, the product is 0.
 a∙0=0
10) Additive Inverse:
 The opposite of a number. The sum of a number and its additive inverse is 0.
 The additive inverse of 5 is negative 5 because 5 + (-5) = 0
x + (-x) = 0
11) Multiplicative Inverse:
 The reciprocal of a number. The product of a number and its multiplicative inverse is 1.

1
1
The multiplicative inverse of 5 is 5 because 5 (5) = 1
1
𝑥 (𝑥) = 1
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Real Numbers and Properties
1B
Numbers Worksheet
Part 1 – Use an integer to express the number(s) in each application below:
1) Erin discovers that she has spent $53 more than she has in her checking account.________
2) The record high Fahrenheit temperature in the United States was 134˚ on July 10th, 1913. ________
3) A football team gained 5 yards _________, then lost 10 yards on the next play ________
4) The shore surrounding the Dead Sea is 1348 feet below sea level. ___________
Part 2 – Tell whether each statement is true or false. (write the entire word)
5) - 2 < 4
____________
6) 6 > - 3
____________
7) - 9 < - 12 ____________
8) - 4 ≥ - 1
____________
9) - 6 ≤ 0
10) - 15 > - 5 ____________
____________
Part 3 – Write an example of a number that satisfies each given condition.
11) An integer between 3.6 and 4.6 ____________
12) A rational number between 2.8 and 2.9 ____________
13) A whole number that is not positive and is less than 1 ____________
14) A whole number that is greater than 3.5 ___________
15) A real number that is neither negative nor positive ____________
Part 4 – Circle the correct answer to the following questions.
______16) Which number is a whole number but not a natural number?
a) – 2
b) 3
c) ½
d) 0
______17) Which number is an integer but not a whole number?
a) – 5
b) ¼
c) 3
d) 2.5
______18) Which number is irrational?
a) 𝜋
b) 4
c) .1875
d) .33
Part 5 – Write an example down for the following questions.
19) Give an example of a number that is rational, but not an integer.
20) Give an example of a number that is an integer, but not a whole number.
21) Give an example of a number that is a whole number, but not a natural number.
22) Give an example of a number that is a natural number, but not an integer.
___________
Properties Worksheet
A. Complete the Matching Column (put the corresponding letter next to the number)
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
If 18 = 13 + 5, then 13+5 = 18
6 · (2 · 5) = (6 · 2) · 5
3(9 + 2) = 3(9) + 3(2)
15 + (10 + 3) = (15 + 10) + 3
50 · 1 = 50
7∙4=4∙7
13 + 0 = 13
11 + 8 = 11 + 8
If 30 + 34 = 64 and 64 = 82, then 30 + 34 = 82
11 ∙ 0 = 0
a) Reflexive
b) Additive Identity
c) Multiplicative identity
d) Associative Property of Mult.
e) Transitive
f) Associative Property of Add.
g) Symmetric
h) Commutative Property of Mult.
I) Multiplicative property of zero
j) Distributive
______ 11) Which property is represented by: 5+ (4 + 7x) = (5 + 4) + 7x?
a) Associative Property of Add.
c) Distributive Property
b) Commutative Property of Add.
d) Symmetric Property
______ 12) Which property is illustrated by 5(a + 6) = 5(a) + 5(6)
a) associative prop. of add.
b) distributive
c) transitive
d) symmetric
______ 13) What is the formula for area of a rhombus?
a) A = lh
b) A = ½ h(b1 + b2)
d) A = lwh
c) A = ½ d1d2
______ 14) What property is represented by: If 4 + 14 = 18 and 18 = 6 ∙ 3, then 14 + 4 = 6 ∙ 3 ?
a) Symmetric Property
c) Commutative Property of Add.
b) Transitive Property
d) Awesome Property
______ 15) Which property is represented by: 3 + 9 = 9 + 3?
a) Transitive Property
c) Reflexive Property
b) Symmetric Property
d) Commutative Property of Add.
______ 16) Which property is represented by: If 3 + 11 = 14, then 14 = 3 + 11?
a) Transitive Property
c) Reflexive Property
b) Commutative Property of Add.
d) Symmetric Property
17) Write a statement that illustrates the Additive Identity Property:
______________________________
18) Write a statement that illustrates the Multiplicative Identity Property:
19) Write a statement that illustrates the Symmetric Property:
________________________
______________________________
20) Write a statement that illustrates the Associative Property of Add.: ______________________________
Name____ANSWERS_______________________
Algebra I – Pd ____
Date_________________________
Real Numbers and Properties
1B
Numbers Worksheet
Part 1 – Use an integer to express the number(s) in each application below:
1) – 53
3) 5, −10
2) 134
4) −1348
Part 2 – Tell whether each statement is true or false. (write the entire word)
5) True
6) True
7) False
8) False
9) True
10) False
Part 3 – Write an example of a number that satisfies each given condition.
11) 4
12) 2.81
13) 0
14) 4
15) 0
Part 4 – Circle the correct answer to the following questions.
16) D
17) A
18) A
Part 5 – Write an example down for the following questions.
19) Decimal or Fraction
20) negatives
21)zero
22) not possible
Properties Worksheet
Matching Column:
1) G 2) D
3) J
Multiple Choice:
11) A
12) B
4) F
5) C
13) C
6) H
7) B
8) A
14) B
17) Write a statement that illustrates the Additive Identity Property:
9) E
15) D
16) D
______________________________
18) Write a statement that illustrates the Multiplicative Identity Property:
19) Write a statement that illustrates the Symmetric Property:
10) I
________________________
______________________________
20) Write a statement that illustrates the Associative Property of Add.: ______________________________
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Real Numbers and Properties
1C
Directions: You may answer of all the following questions on this paper.
1) State which property is being shown
a) 3(x + 5) = 3x + 3(5)
b) (9 + 4) + 5 = 9 + (4 + 5)
c) 36 ∙ 0 = 0
d) 8m + 6m = m(8 + 6)
e) (m ∙ 14) ∙ n = m ∙ (14 ∙ n)
f) 162 ∙ 1 = 162
1
g) 4 ∙ ( ) = 1
4
h) 5 + 8 = 8 + 5
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
2) Complete the matching column
_____1) 5(6 + 2) = 5(6) + 5(2)
_____ 2) If 40 = 4(10), then 4(10) = 40
_____ 3)5 + 18 = 18 + 5
_____ 4) 14 · 1 = 14
_____ 5) 15 + 2 = 15 + 2
_____ 6)(5 + 6) + 8 = 5 + (6 + 8)
_____ 7) If 62 = 36 and 36 = 4(9), then 62 = 4(9)
_____ 8) 23 · 0 = 0
a) Additive Identity
b) Associative Property of Mult.
c) Commutative Property of Add.
d) Distributive Property
e) Transitive Property
f) Multiplicative Identity
g) Associative Property of Add.
h) Multiplicative property of Zero
I) Commutative Property of Mult.
j) Symmetric Property
k) Reflexive Property
3) Is the following operation true? If true, which property is being show, if false, explain why.
(8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
_____ 4) Which is an illustration of the commutative property of addition?
a) a + 0 = a
b) a(b + c) = ab + ac
c) a + b = b + a
d) (a + b) + c = a + (b + c)
_____ 5) Which statement illustrates the associative property of multiplication?
1
a) 2 (2) = 1
c) 2(3 · 4) = (2 · 3)4
b) 2(3 + 4) = 2(3) + 2(4)
d) 2(1) = 2
6) Give an example of each:
a) a number that is whole, but not a natural number
___________________________
b) a number that is rational, but not a whole number
___________________________
c) a number that is rational, but not an integer
___________________________
d) a number that is irrational
___________________________
e) a number that is a natural number, but not an integer
___________________________
f) a number that is an integer, but not a natural number
___________________________
7) Write True or False (do not write T or F… you must write out the whole word!)
a) all whole number are rational
_____________________
b) all integers are natural numbers
_____________________
c) all real numbers are rational
_____________________
d) all irrational number are real
_____________________
e) all natural numbers are irrational
_____________________
Name____ANSWERS___________________________
Algebra I – Pd ____
Date_________________________
Real Numbers and Properties
1C
1) State which property is being shown
a) Distributive property
b) Assoc. Prop. Of Add.
d) Distributive Property
e) Assoc. Prop. Of Mult.
g) Multiplicative Inverse
h) Comm. Prop of Add.
c) Multi. Prop of Zero
f) Multi. Identity
2) Complete the matching column
1) D
2) J
6) G
7) E
5) K
3) C
8) H
4) F
3) (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2)  False
4) C
5) C
6) Give an example of each:
7)
a) a number that is whole, but not a natural number
Zero
b) a number that is rational, but not a whole number
Negatives or Decimals
c) a number that is rational, but not an integer
Decimals or Fractions
d) a number that is irrational
𝝅
e) a number that is a natural number, but not an integer
Not possible
f) a number that is an integer, but not a natural number
Negatives or Zero
a) True
b) False
c) False
d) True
e) False
√𝟐
√𝟑
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Evaluating Expressions
1D
When given an algebraic expression with one or more unknown variables, we cannot find the
exact value of the expression. If we are told what the value(s) or the variable(s) are then we can find
the exact value.
For Example: 13x + 2y
Since we do not know the values of x and y we cannot simplify
If we are told to evaluate 13x + 2y when x = 3 and y = 4, we can substitute these values in.
First step:
Write the expression
Second step: Replace the variables
Third step:
Simplify using PEMDAS
13x + 2y
13(3) + 2(4) ** Always use parenthesis
39 + 8 = 47
Errors often occur due to sloppiness and laziness, so be careful and be neat!!
Directions: Evaluate the following
1) 50 – 3x, when x = 7
1) _______________
2) 2𝑥 2 − 5𝑥 + 4 when x = 7
2) _______________
3)
2𝑎
5
+ (𝑛 − 1)𝑑 when a = 40, n = 10 and d = 3
4) (2𝑥)2 − 2𝑥 2 when x = 4
3) _______________
4) _______________
1
5) 𝑥 2 − 8𝑦 when x = 5 and y = 2
5) _______________
6) 𝑟 2 + 4𝑠 when r = 3 and s = 0.5
6) _______________
7) 𝑎2 + 𝑏 2 − 𝑑 2 when a = 8, b = 6, and d = 3
7) _______________
8) (3𝑤 − 2𝑥)2 when w = 10 and x = 8
8) _______________
9) 3𝑤 2 − 2𝑥 2 when w = 10 and x = 8
9) _______________
10)
11)
5
9
1
2
(𝐹 − 32) when F = 86
10) _______________
𝑥(𝑦 + 𝑧) when x = 8, y = 5, and z = 2
11) _______________
Extra Examples:
Part 1 – Using your order of operations evaluate the expression.
1) 5 + 2 – 3
2) 12 – 6 + 1
3) 10 · 2 ÷ 4
4) 4 + 3 · 2
5) 8 · 3 – 10
6) 5 – 14 ÷ 7
7) 2 + 36 ÷ 4
8) 10 ÷ 5 + 3 · 2
9) 4 – 20 ÷ 10 + 7
10) 3 · 22 + 1
11) 2 · 32 ÷ 3
12) 4(2 + 3) – 8
Part 2 – Using the given information, evaluate the expression.
13) 3 + 2x2, when x = 2
14) 30 – 3x2, when x = 3
15) 3a – 2b, when a = 2 and b = 3
16) 5x2 – y, when x = 3 and y = 5
17) 2x + x2 – 4, when x = 4
18) a3 – 3a + 5, when a = 2
19) a2 ÷ 5 + 3, when a = 5
20) x · y – 8, when x = 3 and y = 4
21) a2 – b ÷ 4, when a = 5 and b = 8
22) 3y – x2 · 4, when x = 2 and y = 6
23)
2𝑎+𝑏
3
when a = 4 and b = 1
𝑥
24) 7 – 𝑦 · 2, when x = 15 and y = 5
25)(2y + 6) – 4y, when y = 3
26) 5c – (2 + c), when c = 2
27) 2b(7 + b), when b = 1
28) (3x + 1)x, when x = 3
29) 3x(2y – 3), when x = 5 and y = 2
30) 3x + 2(2x + 5), when x = 1
31) 15 ÷ (2a + 1), when a = 1
32) (7x + 4) ÷ 2, when x = 2
33) x ÷ (2y + 1), when x = 21 and y = 1
34) b ÷ (3a – 2), when a = 2 and b = 16
35) (6a + 2) ÷ b, when a = 3 and b = 2
36) [10 – (2x ÷ 3)] + y, when x = 3 and y = 4
37)
38)
39)
8𝑎2 − 10𝑏 ÷(3𝑐)+ 4
2𝑏2 ÷(3𝑎−9)
when a = −3, b = 6, and c = 2
[2𝑦 2 +8𝑥 2 ÷(−10)]÷3𝑧
4𝑥+6𝑦+8𝑦+2
(𝑎2 + 𝑏2 )÷(5𝑐)
10𝑏−7𝑎−1
when x = 5, y = 7, and z = −4
when a = −8, b = −6 and c = 4
Name________ANSWERS_______________________
Algebra I – Pd ____
Date_________________________
Evaluating Expressions
1D
Directions: Evaluate the following
1) 29
2) 67
3) 43
4)31
5) 21
7) 91
8) 196
9) 172
10) 30
11) 28
6) 9.2
Extra Examples:
Part 1 – Using your order of operations evaluate the expression.
1) 4
2) 7
3) 5
4) 10
5) 14
6) 3
7) 11
8) 8
9) 9
10) 13
11) 6
12) 12
Part 2 – Using the given information, evaluate the expression.
13) 11
14) 3
15) 0
16) 40
17) 20
18)7
19) 8
20) 4
21) 23
22) 2
23) 3
24) 1
25) 0
26) 6
27) 16
28) 30
29) 15
30)17
31) 5
32) 9
33) 7
34) 4
35) 10
36) 12
37)
38)
39)
8𝑎2 − 10𝑏 ÷(3𝑐)+ 4
2𝑏2 ÷(3𝑎−9)
when a = −3, b = 6, and c = 2
[2𝑦 2 +8𝑥 2 ÷(−10)]÷3𝑧
4𝑥+6𝑦+8𝑦+2
(𝑎2 + 𝑏2 )÷(5𝑐)
10𝑏−7𝑎−1
when x = 5, y = 7, and z = −4
when a = −8, b = −6 and c = 4
−
𝟑𝟑
𝟐
𝟏𝟑
− 𝟏𝟓
−𝟏
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Combining Like Terms
1E
Simplifying and Combining Like Terms
Exponent
2
Coefficient
4x
* Write the coefficients, variables, and exponents of the following:
Coefficients
Variables
Exponents
Variable (or Base)
8c2
9x
y8
12a2b3
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)).
When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and
adding or subtracting the numerical coefficients.
Examples:
3x + 4x = 7x
13xy – 9xy = 4xy
12x3y2 - 5x3y2 = 7x3y2
Why can’t you simplify?
4x3 + 4y3
Simplify the following:
1) 7x + 5 – 3x
4) (12x – 5) – (7x – 11)
11x2 – 7x
6x3y + 5xy3
2) 6w2 + 11w + 8w2 – 15w
3) 6x + 4 + 15 – 7x
5) (2x2 - 3x + 7) – (-3x2 + 4x – 7)
6) 11a2b – 12ab2
WORKING WITH THE DISTRIBUTIVE PROPERTY
Example:
3(2x – 5) + 5(3x +6) =
Since in the order of operations, multiplication comes before addition and subtraction, we must get rid of the
multiplication before you can combine like terms. We do this by using the distributive property:
3(2x – 5) + 5(3x +6) =
3(2x) – 3(5) + 5(3x) + 5(6) =
6x - 15 + 15x + 30 =
Now you can combine the like terms:
Final answer:
6x + 15x = 21x
3(2x – 5) + 5(3x + 6) = 21x + 15
-15 + 30 = 15
Combining Like Terms Examples:
1) (7𝑥 + 8) + (5𝑥 − 10)
2) (2𝑥 − 5) + (6 + 3𝑥)
3) (9 − 3𝑥) − (−6𝑥 + 7)
4) (7𝑥 + 9) − (8 − 2𝑥)
5) (13𝑢 − 9) + (8𝑢 + 17)
6) (19𝑎 − 5) − (6𝑎 − 11)
7) (7𝑐 2 − 5𝑐 + 10) − (7𝑐 2 − 9𝑐)
8) (16𝑐 2 − 8 + 13𝑐) + (9 − 4𝑐 2 + 7𝑐)
9) (7𝑛 − 13) − (19𝑛2 − 15 + 12𝑛)
10) (22𝑥 2 − 13𝑥 + 7) + (−9𝑥 2 + 21𝑥 − 7)
11) (4𝑥 2 − 8𝑥 + 3) + (6𝑥 2 − 4𝑥 + 11)
12) (𝑥 2 − 13𝑥 + 7) − (3𝑥 2 − 4 − 20𝑥)
13) (7 + 𝑥 2 − 4𝑥) + (10𝑥 2 + 9𝑥 − 5)
14) (15 + 10𝑥 + 7𝑥 2 ) − (−6𝑥 − 10𝑥 2 + 9)
15) (3𝑦 2 − 5𝑦 + 10) + (7𝑦 2 − 13𝑦 + 24)
16) (−6𝑎2 + 4 − 9𝑎) − (5 − 4𝑎2 + 7𝑎)
17) (3𝑏 4 + 2𝑏 2 − 8𝑏 + 14) + (3𝑏 4 + 16𝑏 − 11)
18) (25𝑧 2 − 9) − (15𝑧 2 + 7𝑧 − 20)
19) (6𝑘 3 − 4𝑘 2 + 7𝑘 + 1) − (4𝑘 3 − 3𝑘 2 + 6𝑘 + 1)
20) (6𝑥 2 + 13𝑥𝑦 − 5𝑦 2 ) + (9𝑥𝑦 − 2𝑥 2 + 3𝑦 2 )
21) (5𝑥𝑦 + 6𝑥 2 𝑦 − 4𝑦 2 𝑥) + (9𝑥 2 𝑦 − 5𝑥𝑦 + 10𝑥𝑦 2 )
22) (2𝑥 + 8) − (3𝑥 2 + 5𝑥 − 16)
23) (3𝑥 + 7𝑦 − 5) − (2𝑥 2 − 9𝑥 + 12)
24) (3𝑦 − 9𝑥 + 7) − (15 + 8𝑦 − 13𝑥)
25) (15𝑥𝑦 − 6𝑥 2 𝑦 + 9𝑦 2 𝑥) − (9𝑥 2 𝑦 + 11𝑥𝑦 − 4𝑥𝑦 2 )
26) (5𝑧 2 + 10𝑧) − (−15𝑧 2 − 18 + 9𝑧)
Distributive Property Examples:
1) 4(7𝑥 − 8) + 6(5𝑥 + 10)
2) 6(4𝑥 2 – 5𝑥 + 2) + 3(−8𝑥 2 + 11𝑥 + 4)
3) 5(4𝑥 2 – 8𝑥 + 3) – 7(6𝑥 2 – 4𝑥 + 11)
4) 4(6𝑥 3 – 4𝑥 2 + 1) – 9(4𝑥 3 – 2𝑥 2 + 1)
5) 10(4𝑥 2 + 8𝑥 + 7) – 8(5𝑥 2 + 10𝑥 – 9)
6) 6(4𝑥 2 – 3𝑥 + 2) + 5(3𝑥 – 6)
7) 9(4𝑥 2 – 7𝑥 + 12) – 12(3𝑥 2 – 5𝑥 – 9)
8) 4(6𝑥 3 – 4𝑥 2 + 11) – 7(5𝑥 2 + 9)
9) 7(9𝑥 + 3𝑦) + 4(2𝑥 + 6)
10) 8( 4𝑥 2 – 3𝑥) + 5 (6𝑥 – 7)
11) 6(3𝑥 + 8) + 4 ( 2𝑥 2 + 9)
12) 5(3 + 7𝑦) + 6(8𝑦 – 4𝑦 2 )
13) 7( 2𝑥 + 8) – 4(3𝑥 2 + 5𝑥 – 6)
14) 9(3𝑥𝑦 + 7𝑦 – 5) + 5(3𝑦 2 + 6)
15) 5( 3𝑦 2 + 7𝑦 – 10) + 6(2𝑦 2 – 8𝑦 + 6)
16) 3(7𝑥 + 2𝑦 – 8) – 5(9𝑥 + 4𝑦 – 11)
17) 3(12𝑥 4 – 16𝑥 3 + 4𝑥 2 – 8𝑥 + 24) – 4(9𝑥 4 – 12𝑥 3 – 3𝑥 2 – 6𝑥 + 18)
Combining Like Terms Examples: ANSWERS
1) 12x -2
2) 5x +1
3) 3x + 2
4) 9x + 1
5)21u + 8
6) 13a + 6
7) 4c + 10
8) 12c2 + 20c + 1
9) -19n2 - 5n + 2
10) 13x2 + 8x
11) 10x2 – 12x + 14
12) -2x2 + 7x + 11
13) 11x2 + 5x + 2
14) 17x2 + 16x + 6
15) 10y2 - 18y + 34
16) -2a2 - 16a – 1
17) 6b4 + 2b2 +8b + 3
18) 10z2 – 7z + 11
19) 2k3 – k2 + k
20) 4x2 – 2y2 + 22xy
21) 15x2y + 6xy2
22) -3x2 – 3x + 24
23) -2x2 + 12x + 7y -17
25) -15x2y + 13xy2 4xy
26) 20z2 + z + 18
Distributive Property Examples: ANSWERS
1) 58𝑥 + 28
2) 3𝑥 2 + 24
3) −22𝑥 2 − 12𝑥 − 62
4) −12𝑥 3 + 2𝑥 2 − 5
5) 142
6) 24𝑥 2 − 3𝑥 − 18
7) −3𝑥 + 216
8) 24𝑥 3 − 51𝑥 2 − 19
9) 71𝑥 + 21𝑦 + 24
10) 32𝑥 2 + 6𝑥 − 35)
11) 8𝑥 2 + 18𝑥 + 84
12) −24𝑦 2 + 77𝑦 + 15
13) −12𝑥 2 − 6𝑥 + 80
14) 27𝑥𝑦 + 15𝑦 2 + 63𝑦 − 15
15) 27𝑦 2 − 13𝑦 − 14
16) −24𝑥 − 14𝑦 + 31
17) 24𝑥 2
24) 4x – 5y – 8
Name __________________________________________
Algebra I – Pd ______
Date ________________________
Solving Basic Equations
1F
Solving Equations
Golden Rule of Algebra:
“Do unto one side of the equal sign as you will do to the other…”
**Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you
multiply by -2 on the left side, you have to multiply by -2 on the other. If you subtract 15 from one side, you
must subtract 15 from the other. You can do whatever you want (to get the x by itself) as long as you do it on
both sides of the equal sign.
Solving Single Step Equations:
To solve single step equations, you do the opposite of whatever the operation is. The opposite of
addition is subtraction and the opposite of multiplication is division.
Solve the following equations for x:
1)
x + 5 = 12
2)
4)
5x = -30
5)
7)
x + 15 = 28
8)
15 – x = 21
9)
10)
6 + x = 34
11)
9x = 45
12)
x – 11 = 19
𝑥
−5
=3
3)
6)
22 – x = 17
2
3
x=-8
𝑥
4
=5
7 + x = 19
Solving Multi-Step Equations:
3x – 5 = 22
+5
+5
PEMDAS***
3x = 27
3
3
x = 9
To get the x by itself, you will need to get rid of the 5 and the 3.
Get rid of addition and subtraction first.
***Use the opposite order of
Then, we get rid of multiplication and division.
We check the answer by putting it back in the original equation:
Check:
3x – 5 = 22
We have that x = 9
3(9) - 5 = 22
27 - 5 = 22
22 = 22 (It checks!)
Directions: Solve and check the Multi-Step Equations on looseleaf.
−𝑥
5
1) 9x - 11 = -38
2) 160 = 7x + 6
3)
4) ¾x - 11 = 16
5) 4x – 7 = -23
6) 26 = 60 – 2x
7) 21 – 4x = 45
8)
10) 2x + 8 = 34
11) 15 = 3x – 9
12) 33 = 3 – 10x
13) 6x + 15 = 51
14) 19 + 8x = 43
15)
𝑥
7
-4=4
+3 = 7
9) ½ x – 5 = 9
𝑥
3
+ 15 = 48
Name __________________________________________
Algebra I – Pd ______
Date ________________________
Solving Basic Equations
1F
Solving Equations
Front ANSWERS:
1) x = 7
2) x = 30
3) x = 5
4) x = -6
5) x = -15
6) x = -12
7) x = 13
8) x = -6
9) x = 20
10) x = 28
11) x = 5
12) x = 12
1) x = -3
2) x = 22
3) x = -20
4) x = 36
5) x = -4
6) x = 17
7) x = -6
8) x = 56
9) x = 28
10) x = 13
11) x = 8
12) x = -3
13) x = 6
14) x = 3
15) x = 99
Back ANSWERS:
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Like Terms & Basic Equations
Directions: Do all problems on looseleaf.
Part 1 – Simplify the following expression. (Remember to show your RAINBOW!!)
1) 3(5x – 3) + 6(2x + 4)
2) 7(2x2 – 6x + 2) + 3(−5x2 + 14x – 4)
3) 9(7x2 – 5x + 9) – 7(8x2 – 3x + 12)
4) 6(3x3 – 4x2 + 11x – 5) – 10(−2x3 – 6x2 + 6x +7)
5) 4(2x2 + 6x + 5) – 8(x2 + 3x – 5)
6) 7(4x2 – 3x + 2) + 9(3x – 6)
7) 12(3x2 – 6x + 9) – 9(4x2 – 8x – 12)
8) 5(6x3 – 4x2 + 11) – 6(5x2 + 9)
9) 10(3x4 – 5x3 + 7x2 – 10x + 6) – 5(6x4 – 10x3 – 14x2 – 20x + 12)
Part 2 – Solve for x and check your answers.
1) 2x + 9 = 15
2) 7x – 6 = 29
3) 24 – 2x = −12
4)
5) 12x + 2 = −34
6) 62 – 4x = 70
7) 88 – 11x = 0
8) 15 = 24 + 3x
9) 13.5x + 2 = −25
10) 6x + 2 = 30
11) 2.5x – 9 = 18.5
12) 4x – 12 + 2x = 42
𝑥
5
−6 = − 8