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Algebra Lesson #1: Solving Linear Equations (I)
Algebra
Lesson 1:
Solving Linear Equations (I)
(Solving 2- Step Equations)
Before we get into solving equations, we need to review some basic terms from
Grade 8 and 9 algebra:
 Algebra is just a division of Mathematics that deals with performing operations
(add, subtract, etc.) on both numbers, and variables (_________). There are two
basic groupings of terms we perform algebra on:
Equations
Expressions
- A collection of numbers and letters
with an equals (=) sign. ** Can be
solved for variables
Ex:
2x  3  4 , 5 y  3x  2 x  4
___________________
___________________
- A collection of numbers and letters without
an equals (=) sign. ** Can be simplified not
solved **
Ex: 5 x  2 y  z , 2 x 2  4 xy  7 y 2
_____________________
_____________________
Each equation or expression can be split up into _______________. These are
collections of numbers and variables that are __________ or __________
together. They are separated by ____________ or _______________ signs.
Look at the following algebraic expression. Connect the proper word to the
appropriate letter or number with an arrow:
Term
Constant
5x  3 y  7
Coefficient
Variable
Now we’ve talked about some basic terms, let’s try and solve some equations.
When solving equations, you are trying to isolate the variable. This just means
to ____________________________________.
In order to do that, we need to follow two simple commandments:
1. Thou Shalt Always Perform the Same Operation To Both Sides of
the Equation
2. Thou Shalt Always Perform the Opposite Operation
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Algebra Lesson #1: Solving Linear Equations (I)
Let’s try to follow the above rules on some simple questions:
Ex 1: Solve for x:
a)
** Isolate for _____, so you need to move _____
12x  132
____ is being _____ by x, so _____ to get rid of it.
Make sure you ______ on both sides
Check:
b)
58  x 112
Check:
** Substitute the answer back into the original equation
To be sure that the left side _______ the right side
** Isolate for _____, so you need to move _____
____ is being _____ by x, so _____ to get rid of it.
Make sure you ______ on both sides
** Substitute the answer back into the original equation
To be sure that the left side _______ the right side
Now, let’s try Two – Step problems. To do these, you work to get rid of numbers
opposite to the BEDMAS order. ie. You work in SAMDEB (Subtraction/Addition
first, then Multiplication/Division, then Exponents, and finally Brackets)
It is easier to remember this saying:
“Work your way into the x … Get rid of outside numbers FIRST”
Ex 2: Solve for the variable:
2 y  15  32
a)
Check:
b)
35  4x  7
Check:
c) 7  a  12
Check:
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Algebra Lesson #1: Solving Linear Equations (I)
Ex 3: The time required for a car to travel 800 km away from Maple Ridge is
given by the equation 70t 170  800 . Find the time ( t ):
Assignment:
1. Classify each as an expression or an equation. Then, identify the
variables, coefficients, and constants in each (if appropriate).
3
a. 6 y  4 x 2  2 xy
b. 3 x  y  2
c. 0  3x  2 y  4
5
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
d. 5ab  7cd
e.
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
3a  7ab  2
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
f. 2 x  5  7 x  3 y
Expression/Equation:__________
Variables:___________________
Coefficients:_________________
Constants:__________________
2. Solve each of the following. Make sure to show check in the appropriate
place:
a. 4q  9  15
b. 11w 60  16
c. 6e  7  5
Check:
4q  9  15
Check:
11w 60  16
Check:
6e  7  5
d. u  24  7
e. 9t  2  56
f. 23  g  13
Check:
u  24  7
Check:
9t  2  56
Check:
23  g  13
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Algebra Lesson #1: Solving Linear Equations (I)
g. 69  7v  6
h. 67  6i 1
i. 35  2t 15
Check:
69  7v  6
Check:
67  6i 1
Check:
35  2t 15
j. 4 y  9  19
k. 4  3n  43
Check:
4 y  9  19
Check:
4  3n  43
l. 8  32  5b
Check:
8  32  5b
3. The time required for a car to travel to Maple Ridge is given by the
equation 400  25t  0 . Find the time (t):
4. The number of tickets (n) required to make a $400 000 profit at a concert
is given by the equation: 50n  30000  40000 . Find the number of tickets
(n):
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Algebra Lesson #1: Solving Linear Equations (I)
5. Jimmy was constantly whining to play with his brother Jonny’s baseball.
To shut him up, Jonny said “ You can play with it if you can tell me a
number that when doubled, and decreased by 14 is equal to 32.” Jimmy
couldn’t figure it out, can you?
6. Solve the following equations, then put the corresponding letter above the
blank with its solution to “break the code”. (No checks necessary)
E. 12  5u  48
N. 6 10k  256
O. 27  20v  73
D. 100  12 y  4
R. 13  5  8o
U. 36  x  36
___ ___ ___ ___ ___ ___
72
-1 -8
5
25
12
Answer Key:
2a. 6 2b. –4 2c. –2 2d. 17 2e. –6 2f. 10 2g. –9 2h. –11 2i. –25 2j. –7 2k. –132 l. 8 3. 16 4. 200
5. 23