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Math 7 Study Guide
Unit 2: Expressions and Equations
Name:
Skills and Application Section (Multiple Choice)
1. Simplify: 7 − 9𝑥 − 4𝑥
2. Simplify: 4(1 − 10𝑥)
3. Simplify: −9(7 + 𝑥) − 6𝑥
4. Solve for x:
𝑥
2
= −14
5. Solve for x: 3𝑥 − 6 = 15
6. Solve for x: 5(𝑥 − 3) = 15
7. Solve and graph the inequality: −2𝑥 + 3 > 21
8. Solve and graph the inequality: −2 +
𝑛
20
≤ −3
9. Write an equation that represents: Eight more than the product of a number and two is equal to forty-nine
10. Write an expression that represents: Six more than the quotient of a number and five
11. The Eagles scored (8n - 6) points. The Rockets scored (5n + 4) points. Write an expression to show how many more
points the Eagles scored than the Rockets.
12.
13. Write an equation and solve it:
Abby bought 3 sweaters that each cost the same amount and 1 skirt that cost $15. The items she bought cost a total
of $90 before tax was added. What was the cost of each sweater?
14. The interior (inside) angles of a triangle add up to equal 180.
Write an equation and solve it to find the value of x.
15. Paul paid $10 for a ticket to the fair and then another $2 per ride. Write an equation to show how many rides x, Paul
can take if he has $40.
16. Michelle paid a total of $48 for 4 pizzas. She used a coupon for $4 off the entire order. The equation below can be
used to determine the regular price of one pizza, p.
4p - 4 = 48
What is the regular price of one pizza?
17. Bella had a party at the arcade. It cost $29 for laser tag and $5.50 per friend for game cards. How many friends did
Bella have at her party if she spent $110?
18. Mr. Grant needs at least 55 paintbrushes for his art classes. He has 25 paintbrushes already and will buy more
paintbrushes in packages of 6. Write an inequality that can be used to find how many packages of paintbrushes, p,
Mr. Grant needs to buy in order to have at least 55 paintbrushes?
19. Craig went bowling with $30 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the
greatest number of games Craig could have played? Write an inequality and solve it.
20. Angela needs to load some boxes on an elevator. The maximum weight the elevator can hold is 2,000 pounds. If
Angela weighs 130 pounds and each box weighs 90 pounds, what is the maximum number of boxes Angela can
bring on the elevator with her? Write an inequality and solve it.
Knowledge and Understanding Section (Extended and Constructed Response)
1.
Write an equation or expression and label with the following vocabulary words:
Constant
Variable
Coefficient
Term
2.
Explain and demonstrate how to check the solution of an equation using the following problem.
−2𝑥 + 3 = 5
−3 − 3
−2𝑥 = 2
−2 − 2
𝑥 = −1
3.
Explain the difference between the solutions to 2 x  3  11 and 2 x  3  11.
4.
Explain how to solve an equation using two steps. Use precise math vocabulary and complete sentences.
5.
You have $70 to spend on clothes. Jeans cost $29 and t-shirts cost $8 without any added tax.
1.
Write and solve an inequality to find out how many pairs of jeans you can purchase if you buy (1) t-shirt.
Explain your solution.
2.
Write and solve a second inequality to find out how many t-shirts you can purchase if you buy (1) pair of jeans. Explain
your solution.