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Ignition Learning — Activity Sheet

Solving simple equations

Mathematics · Year 7

Name: ______________________Date: ____________

An equation is a mathematical statement that two things are equal, like "x + 5 = 12". To solve it, you work out what value of the pronumeral (like x) makes the equation true, by doing the same operation to both sides to keep it balanced. If a number is added, subtract it from both sides; if multiplied, divide both sides; and so on, working step by step until the pronumeral is alone. You can always check your answer by substituting it back into the original equation.

Example

To solve x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7. Check: 7 + 5 = 12 ✓.

Key terms

Equation:: A statement that two expressions are equal.
Solve:: To find the value of the pronumeral that makes an equation true.
Balance:: Keeping both sides of an equation equal by doing the same thing to each side.

Questions

1. An equation states that two things are:
- Different
- Equal
- Multiplied
- Unknown
2. To solve x + 3 = 10, you:
- Add 3 to both sides
- Subtract 3 from both sides
- Multiply both sides by 3
- Divide both sides by 3
3. What is x if x + 3 = 10?
- 3
- 7
- 10
- 13
4. What is x if x - 4 = 6?
- 2
- 6
- 10
- 24
5. What is x if 3x = 12?
- 3
- 4
- 9
- 36
6. What is x if x/2 = 5?
- 2.5
- 5
- 7
- 10
7. To keep an equation balanced, whatever you do to one side you must:
- Ignore on the other
- Do the opposite on the other
- Do the same on the other
- Multiply the other by 2
8. Solve: x + 8 = 15
- x=7
- x=23
- x=8
- x=15
9. Solve: x - 5 = 9
- x=4
- x=14
- x=5
- x=45
10. Solve: 4x = 20
- x=4
- x=5
- x=16
- x=24
11. Solve: x/3 = 6
- x=2
- x=3
- x=9
- x=18
12. Solve: 2x + 1 = 11
- x=5
- x=6
- x=10
- x=22
13. Solve: 3x - 2 = 10
- x=4
- x=6
- x=8
- x=12
14. Is x=5 a solution to x + 7 = 12?
- Yes
- No
- Cannot tell
- Only sometimes
15. Solve: 5x + 3 = 28
- x=5
- x=6.2
- x=25
- x=31
16. Solve: 2(x + 3) = 16
- x=5
- x=8
- x=6.5
- x=10
17. Solve: 3x + 4 = x + 12
- x=4
- x=8
- x=2
- x=16
18. A number plus 9 equals 20. What is the number?
- 11
- 9
- 20
- 29
19. Solve: x/4 + 2 = 7
- x=20
- x=5
- x=28
- x=9
20. Solve: 7 - x = 3
- x=4
- x=10
- x=-4
- x=21

Answer key (parent copy)

1. Equal
2. Subtract 3 from both sides
3. 7
4. 10
5. 4
6. 10
7. Do the same on the other
8. x=7
9. x=14
10. x=5
11. x=18
12. x=5
13. x=4
14. Yes
15. x=5
16. x=5
17. x=4
18. 11
19. x=20
20. x=4