Where did my algebra go wrong?

The missing multiplication

Start with 3(x + 2) = 12. Your next line is 3x + 2 = 12. Stop here: the 3 multiplied x, but not the 2.

The brackets contain a whole group. Three copies of (x + 2) contain three x terms and six extra units. Multiply every term inside the brackets, not just the first.

1. Expand the group: 3x + 6 = 12.
2. Subtract 6 from both sides: 3x = 6.
3. Divide both sides by 3: x = 2.
4. Substitute into the original equation: 3(2 + 2) = 12. The left side is 3 × 4, so it matches the right side.

Checking only your last line can miss an earlier error. Return to the original brackets when you substitute.

The negative sign that disappeared

For −2x + 5 = 13, subtracting 5 from both sides gives −2x = 8. That line is correct. Writing x = 4 next is not: the multiplier of x is −2, not 2.

1. Keep the sign attached to its number. Divide both sides by −2.
2. 8 ÷ (−2) = −4, so x = −4.
3. Check the original: −2(−4) + 5 = 13. Two negative factors give positive 8; adding 5 gives 13.

The mistaken positive answer fails the check: −2(4) + 5 = −3, not 13. A substitution check tells you something went wrong; comparing consecutive lines helps you locate where.

Write the operation, not “move it across”

When solving an equation, subtract the same amount from both sides, or divide both sides by the same nonzero number. This preserves equality. “Move the 6” can hide which operation you meant.

For 3x + 6 = 12, write (3x + 6) − 6 = 12 − 6 before simplifying. If you remove 6 on only the left, you change which value of x makes the equation true.

Try it without looking

Solve 2(y + 3) = 14. Name the operation you apply to both sides at each step.

Bring the line you got stuck on

Type the original question and the steps you have tried. For example: “I wrote 3x + 2 = 12 after 3(x + 2) = 12. Which step changed the equation?” Ask for a clue, make the next attempt, then check it against the original problem.

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