Distributing, step by step

3(x + 4) is not 3x + 4, and the child who writes it has not been careless — they multiplied the first term and stopped.

The question

Mia wrote 6(x + 4) + 5(x + 4) = 11x + 24. Which is correct?

Mia wrote 6(x + 4) + 5(x + 4) = 11x + 24. Which is correct?

6(x + 4) + 5(x + 4)
6(x + 4) + 5(x + 4)=6x + 24 + 5x + 20
6(x + 4) + 5(x + 4)=6x + 24 + 5x + 20
6(x + 4) + 5(x + 4)=11x + 44
6(x + 4) + 5(x + 4)=11x + 44
they wrote:11x + 24
  1. Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
  2. On your own, and writing the step nobody writes down: 6(x + 4) + 5(x + 4) becomes 6x + 24 + 5x + 20.
  3. Tidy that up and it is 11x + 44.
  4. Now compare. They wrote 11x + 24, and the first bracket reached its x but not its number — so the correct answer is 11x + 44.

How it works.

  1. 01

    Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.

  2. 02

    On your own, and writing the step nobody writes down: 6(x + 4) + 5(x + 4) becomes 6x + 24 + 5x + 20.

  3. 03

    Tidy that up and it is 11x + 44.

  4. 04

    Now compare. They wrote 11x + 24, and the first bracket reached its x but not its number — so the correct answer is 11x + 44.