➕ Algebra 1 · Equations
Solving One-Step Equations: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
In x − 17 = 11, adding 17 to both sides gives x = 28.
✓ True. Adding 17 undoes the subtracted 17: 11 + 17 = 28. Check: 28 − 17 = 11.
The solution of x + 4 = 9 is x = 13.
✗ False. You must subtract 4, not add it: x = 9 − 4 = 5. The answer 13 comes from adding 4 by mistake.
To solve x/3 = 12, divide both sides by 3.
✗ False. The x is already divided by 3. Undo that by multiplying both sides by 3: x = 36. Dividing again would give x/9 = 4, which is not what you want.
The solution of −4x = 20 is x = −5.
✓ True. Divide both sides by −4: 20 ÷ (−4) = −5. Check: −4 × (−5) = 20.
The solution of −x = 7 is x = 7.
✗ False. A lone minus sign means −1. Multiply both sides by −1 to get x = −7. Check: −(−7) = 7.
You can multiply both sides of an equation by any number except 0 and keep the same solution.
✓ True. Multiplying by a nonzero number never changes the solution. Multiplying by 0 turns both sides into 0 and loses the information.
x = 7 is not a solution of x − 3 = 10.
✓ True. Substitute: 7 − 3 = 4, and 4 is not 10. The solution is x = 13.
You cannot solve 34 = x + 19 because the variable is on the right side.
✗ False. The variable can be on either side. Subtract 19 from both sides to get 15 = x, so x = 15. Check: 15 + 19 = 34.
To solve (4/3)x = 8, you can multiply both sides by 3/4 to get x = 6.
✓ True. 3/4 is the reciprocal of 4/3, and their product is 1. Then 8 × 3/4 = 6. Check: (4/3)(6) = 8.
Every one-step equation has a whole-number solution.
✗ False. For example, 3x = 7 gives x = 7/3, which is not a whole number.