Name _____________________________________________ Date _____________________ Period ________
Math 7
Unit 3 Study Guide - Equations
One and Two Step Equations
Directions: Solve each equation below. Be sure to check each of your answers.
1. v – 10 = - 3
3.
𝑥
5
=3
2. -5p = -40
4. 12 + 𝑚 = 34
𝑥
5. 4 + 3p = 19
6.
7. -6k – 13 = 83
8. -7 = -11 + 5
9. 13 – x = -11
10.
−3
−2=3
𝑣
1
3
𝑥 − 18 = −12
Multi - Step Equations
Directions: Solve each equation below. Be sure to check each of your answers.
11. 8m – 32 + 7m – 34 = 9
12. 2(3w + 5) = 88
13. 2x + 4(x – 3) = 12
14. -4(5h + 2) = -40
15. 28 - 4(r – 5) = -4
16.
1
5
(25 − 15𝑥) + 16 = 30
Equations with Variables on Both Sides
Directions: Solve each equation below. Be sure to check each of your answers.
17. 3v + 2 = 5v
18. 7n – 5 = 10n + 13
19. 5n – 2 = 3n + 6
20. 8y + 4 = 11y – 17
21. m – 1 = 9m + 15
22. 13 – 4x = 1 - x
Writing and Solving Equations
Directions: For each problem below, define x and write an equation to express the situation. Then, solve the
equation.
23. You and your four friends go to Johnny Rockets. You all split the bill evenly. If each person’s share was
$6.50, how much was the original bill?
24. Bob Lablob is on a diet to lose weight. After losing 26 pounds, Bob weighs 231 pounds. What was Bob
Lablob’s weight before his diet?
25. Jayden is making muffins for the class. He already has 5 muffins, but needs to make a total of 61
muffins. If each batch makes 8 muffins, write and solve an equation to determine how many batches
Jayden needs to make.
26. Jake wants to buy a video game that costs $41, but only has $6 in savings. Jake knows he can earn $7
an hour helping his dad file papers. For how many hours will Jake have to file papers?
27. Mark’s parents charge him$2 every time he forgets his homework. Mark had $36 at the beginning of
the school year. How many times did Mark forget to do his homework if he only had $14 at the end of
the year?
28. Molly is ordering some ornaments for her tree. Amazon is charging $0.75 for each ornament and a
$3.00 shipping fee. For how many ornaments can Molly buy for $15?
29. 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
Answer Key
1. v = 7
2. p = 8
3. x = 15
4. m = 22
5. p = 5
6. x = -15
7. k = -16
8. v = 20
9. x = 24
10. x = 18
11. m = 5
12. w = 13
13. x = 4
14. h = 1.6
15. r = 13
16. x = -3
17. v = 1
18. n = -6
19. n = 4
20. y = 7
21. m = -2
22. x = 4
𝑥
23. Let x = How much each person paid; 5 = 6.5; $32.50
24. Let x = Bob’s original weight; x – 26 = 231; 257 pounds
25. Let x = Number of batches Jayden needs to make; 8x + 5 = 61; 7 batches
26. Let x = How many hours Jake has to file papers; 7x + 6 = 41; 5 hours
27. Let x = How many times Mark forgot his homework; 36 – 2x = 14; 11 times
28. Let x = Number of ornaments ordered; 3 + 0.75x = 15; 16 ornaments
29. 4x + 1 + 2x + 3 + 5x = 59; x = 5