Math 8 Unit 2 Equations Study Guide SOL 8.15
Name: ___________________________
Solve the inequalities and equations. Graph the inequalities.
1. x + 2 = –4x + 7
4. 7𝑦 − 4(3y – 5) > 80
7.
3
(2 −
7
3𝑦) = 6
10. 7x – 9 – 5x = 3 – (12 – 2x)
2.
3
4
𝑥 + 5 < 53
5. 3 + 5(𝑑 − 2) = –3d
5
3. −1.1𝑥 − 4 = 1.5
6. 4ℎ − 3 + 2 – h > 0
1
(6𝑥
3
8. – 2 (𝑤 − 1) = 20
9.
11. n – 2(n – 2) = –11
12. 4.1x – 1.3 = 0.7x + 25.9
+ 3) = 2𝑥 − 5
Which property justifies the work between the steps?
13.
2
5
2
5
2
5
2
5
5
2
𝑥+5=9
Given
𝑥 + 5 + (–5) = 9 + (–5)
Subtraction Property of Equality
𝑥 + 0 = 9 + (–5)
______________________
𝑥=4
______________________
∙
2
5
𝑥=4∙
1𝑥 = 4 ∙
𝑥=4∙
5
Multiplication Property of Equality
2
5
______________________
2
5
______________________
2
𝑥 = 10
14.
Simplify
7 + 4( −𝑛 + 3) = 43
Given
7 − 4𝑛 + 12 = 43
_____________________
−4𝑛 + 7 + 12 = 43
_____________________
– 4𝑛 + 19 = 43
Combine Like Terms
– 4𝑛 + 19 – 19 = 43 − 19
Subtraction Property of Equality
– 4𝑛 + 0 = 43 − 19
_____________________
−4𝑛 = 43 − 19
_____________________
−4𝑛 = 24
Simplify
1
1
(− 4) (– 4𝑛) = (− 4)24
1
1
Multiplication Property of Equality
(− 4 ∙ −4) 𝑛 = (− 4)24
_____________________
1𝑛 = −6
_____________________
𝑛 = −6
_____________________
15.
You helped a friend move a short distance
recently. The friend rented a truck for $15 an
hour and rented a dolly for $5. Your friend paid
a total of $80 for the rental. For how long did
you rent the truck?
17.
A boxing club charges nonmembers $14 per
day for equipment rental. Members pay a yearly
fee of $400 and a daily fee of $5 for equipment
rental. Write and solve an equation to determine
how many times members should use the gym to
pay the same total cost as non-members.
16.
A rental car agency charges $12 per day plus
$.10 per mile to rent a certain car. Another
agency charges $15 per day plus $.08 per mile
to rent the same type of car. How many miles
will have to be driven for the cost of a car from
the first agency to equal the cost of a car from
the second agency?
18. Find the perimeter of the square.
19. Find the dimensions of the rectangle if the perimeter equals 50 ft.
Define a variable, write an equation and solve it.
20. The product of a number and 3 is five less than
a number.
21. Half of the sum of n and 3 is two more than a
number.
Write and solve the equation for the following models.
22.
23.