Math 7 NOTES (4.1)
Name ______________________ Block ____
Solving One-Step Equations (SOL 7.14)
The GOAL of solving an equation _______________________________________________________________
To do this you need to _________ what was done to the variable, using _______________________________.
State the INVERSE OPERATIONS
o Add 23
______________________________ _____
o Subtract 18
___________________________________
o Multiply by –15 ___________________________________
o Divide by 8
___________________________________
Addition & Subtraction Equations:
Example 1:
Solve y  3  10
Example 2:
y  3  10
 Where is the variable?
y  3  10
 ___  ___




What was done to it?
How can I undo that?
Apply to BOTH sides.
Simplify (Solve)
CHECK:
CHECK:
y  3  10
____  3 ≟ 10
____  10 
–2 = y – 7
SOLVE:
SOLVE:
y  ____
Solve
Write original equation.
Substitute ____ for y.
Did my solution make the
equation true?
Solve each equation. Check your solution.
Solve
a  6  17
3x2
Check here:
Solve
b  17  12
y  4  6
Check here:
Multiplication & Division Equations:
Example 3:
Solve 8x = 56.
Example 4:
Solution:
Solve
𝒂
𝟓
= 12
Solution:
8x = 56
𝑎
Where is the variable?
What is done to it?
8x = _56_
= 12
5
How can I undo that?
𝑎
•
= 12 •
5
Apply to both sides.
x = _____
a = _____
Solve/Simplify
Check:
Check:
8x = 56
Write original equation.
8(___) ≟ 56
Substitute for variable.
____  56
Is it true?
𝑎
5
(
= 12
)
5
= 12
_____ = 12
Let’s Practice!!
Solve each equation. Check your solution.
Solve
–3a  18
Check here:
Solve
𝑏
−4
4
𝑓
 12
48  6y
3
 121  11a
𝑔
=7
−7
Check here:
Multiplicative Inverses (Reciprocals): When multiplied, the product is one!!
Multiply each number by its reciprocal.
𝟏
𝟓
𝟑
𝟕
𝟑
Solve
𝟓
𝟓
t6
8
𝟓
𝟐
Solve
𝟑
5
𝟐
t6
The coefficient of t is .
3
−
The reciprocal of
𝟑
𝟓
𝟕
t8
is ____.
Multiply each side by
the Multiplicative
Inverse.
t  ____.
Simplify.
t = ____.
Solve.
Solve each equation.
1
7
3
4
t3
1
x=9
– y=
9
t–6
−
4
5
2
4
2
5
15
3
t8
=
3
10
−
t
5
8
3
5
t  –6
k = 25
Review
(–4)3x
–5(7x)
2 (–x)
–8(–4x)
(–2)7a
(–9x)(–4)
–2m (5)
–5 (–3d)
5a(3a)
–6a(4a)
6a(-4a)
(–8a)(–3a)
Evaluate
(4 + 7)2 − (24 – 3)
−|5(-12)|
-42 + (-4)2
Simplify
6 (y – 2=3)
4(7 – n)
–5(s – 5)
–10(3 – p)
Translate each verbal phrase into an algebraic expression or equation.
$15 off the original price is $78.
20 more than some number is equal to 92.
Vocabulary Check:
Operations that “undo” each other are called _____________________________
A mathematical sentence that contains an equal sign is an ____________________
A _______________________ is a number multiplied by a variable in an expression or equation.
A ______________________ is a symbol, usually a letter, used to represent an unknown number.
Math 7 HOMEWORK (4.1)
1. Solve the equations. Check your solutions.
Solve
Check here:
15 = w + 4
–3b = 21
y – 7 = 12
𝑎
=5
−7
Solve
Check here:
a – 2 = 10
1
3
n = –13
–34 =
3
7
𝑦
2
n = 24
4x = -24
w + (-2) = 12
17 + c = 41
–10 + d = –24
𝑎
−9
𝑓
= –11
−11
= 12
–7s = 49
15h = –75
s – 4 = 12
–8 = b – 5
𝑡
−12
ℎ
= 11
8
–14g = –56
= –6
–112 = –8v
Write each verbal sentence as an algebraic equation. Solve the equations.
2. The sum of a number and 16 is equal to –45.
3. The product of –6 and m is 216.
4. The difference of x and 25 is 57.
5. The quotient of z and –10 is equal to 32.
Translate and solve:
6.
Six less than a number is eighteen.
__________________________________________
7.
The number of members divided by 6 is 15.
__________________________________________
Use the Distributive Property to rewrite and simply each expression.
8. 6(z + 4)
9. –7(c + 2)
10. (d + 5)9
11. (h + 8)(–3)