Name _____________________________________________ Date _____________________ Period ________
Math 7 Enriched
Unit 3 Study Guide - Equations
Solving Equations
Directions: Solve each equation below. When necessary, state if the equation results in no solution, two
solutions or infinite solutions.
1.
3.
𝑥
−3
1
4
+ 4 = 16
(8𝑥 − 12) = 6
5. 3x + 4(3x + 7) = 3(5x + 10)
7.
9.
3
4
(12x – 8) = 2(4x – 3) + x
9𝑥−6
3
= 3x – 2
2.
2
3
𝑥 + 2 = 15
4. 5(2x + 6) = -4(-5 – 2x) + 3x
6.
8.
−4𝑥+4
2
2
3
= 6x + 4
1
(9x – 3) = 4(8x – 16)
10. (-3x + 3)2 = x(x – 6) – 10
Writing and Solving Equations
Directions: For each problem below, define x and write an equation to express the situation. Then, solve the
equation.
11. The sum of three consecutive integers is 60. What is the largest of these numbers?
*Consecutive numbers are numbers that come right after each other. For example, 1, 2, and 3, are
consecutive numbers.*
12. Zoe has $50 with her when she goes into Toys R Us to buy Rubik’s cubes for her and her three friends.
After her purchase, she has $6 left over. How much did each Rubik’s cube cost?
13. You want to place a two 24” pictures on a 96” wall so that they are evenly spaced from each other and
from the ends of the wall. How far from the edge of the wall will the edge of each picture be?
14. Cooper’s mom is 42 years old. Her age is 16 years more than twice Cooper’s age. How old is Cooper?
15. The perimeter of the triangle below is 59. Find the value of x. *Note, for this problem, you should not
define x.*
4x + 1
2x + 3
5x
16. To become a member at Planet Fitness, you have to pay a one-time membership fee of $39 and an
additional $12 per month. To become a member at Commitment Fitness, there is no initial
membership fee but a monthly payment of $25 per month. After how many months would the cost of
both gyms be the same?
17. For what value of x would both shapes have the same perimeter? *Note, for this problem, you should
not define x.*
3x
4x + 2
4x + 2
5x
4x
4x
6x + 1
18. The length of a rectangle is 2 less than twice its width. The perimeter of the rectangle is five times its
width. Find the length and width of the rectangle.