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The 3(x − 4) mistake: multiply every term

The number outside the brackets multiplies everything inside, not just the first term.

The fix

3(x − 4) = 3·x − 3·4 = 3x − 12. Writing 3x − 4 means the 3 never reached the 4.

With a negative outside

−2(x − 5) = −2x + 10, because a negative times a negative is positive. The usual slip is −2x − 10.

Catch it in 5 seconds

Put in x = 1. 3(1 − 4) = −9. Now try your line: 3(1) − 12 = −9 ✓, but 3(1) − 4 = −1 ✗. If the numbers don't match, the line is wrong.

All the way through

3(x − 4) = 2x + 5 → 3x − 12 = 2x + 5 → x = 17. Check: 3(17 − 4) = 39 and 2(17) + 5 = 39. ✓