➕ Algebra 1 · Equations
Solving Multi-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
7(x + 1) = 21 is the same equation as 7x + 1 = 21.
✗ False. The 7 multiplies both terms, so 7(x + 1) = 7x + 7. The correct equation is 7x + 7 = 21.
You can start solving 4(x + 5) = 36 by dividing both sides by 4.
✓ True. The parentheses are the whole side, so dividing both sides by 4 gives x + 5 = 9, and x = 4.
−4(x − 2) simplifies to −4x − 2.
✗ False. (−4)(−2) = +8, so −4(x − 2) = −4x + 8.
9x − 4 + x simplifies to 10x − 4.
✓ True. A lone x means 1x, so 9x + 1x = 10x. The −4 stays.
10 − (x + 6) simplifies to 4 − x.
✓ True. The minus flips both signs inside: 10 − x − 6 = 4 − x.
8 − (x − 3) simplifies to 5 − x.
✗ False. The minus flips both signs inside: 8 − x + 3 = 11 − x. The answer 5 − x comes from forgetting to flip the −3.
The solution of x/2 + x/5 = 7 is x = 10.
✓ True. Multiply every term by 10: 5x + 2x = 70, so 7x = 70 and x = 10. Check: 5 + 2 = 7.
To clear the fractions in x/3 + 4 = 5, you multiply the x/3 term by 3 and leave the other terms alone.
✗ False. Every term on both sides must be multiplied: x + 12 = 15, so x = 3. Multiplying only the fraction gives x + 4 = 5, which wrongly gives x = 1.
Distributing a number across parentheses on the left changes the value of that side, so you must also change the right side.
✗ False. Distributing rewrites the left side as an equal expression, so its value stays the same. The right side is left alone.
Checking your answer in the tidied equation is just as good as checking in the original equation.
✗ False. A slip made while tidying carries into the tidied equation, so the check can pass anyway. For example, wrongly writing 3(x + 4) = 21 as 3x + 4 = 21 gives a wrong answer that fits the wrong equation. Only the original exposes it.
If −x = 7, then x = −7.
✓ True. −x means −1 · x, so divide both sides by −1 to get x = −7. Check: −(−7) = 7.