Question

Find the mistakes.
5(1 + 4x) + 2x = 27 - x
*
5 points
Mistake in this step No Mistake in this step
Step 1: Distribute; 5 + 4x + 2x = 27 - x
Step 2: Combine like terms; 5 + 6x = 27 - x
Step 3: Get x's on one side: 5 - 7x = 27
Step 4: -7x = 22
Step 5: x = 22/-7
Step 1: Distribute; 5 + 4x + 2x = 27 - x
Step 2: Combine like terms; 5 + 6x = 27 - x
Step 3: Get x's on one side: 5 - 7x = 27
Step 4: -7x = 22
Step 5: x = 22/-7

Answer 1

All steps shown are incorrect.

Errors:
- Step 1 (and therefore Step 2 onward): Distribution is wrong. 5(1 + 4x) = 5 + 20x, not 5 + 4x.
- Step 2: Wrong combination because of the bad distribution (20x + 2x = 22x, not 6x).
- Step 3: Sign/error moving terms — from 5 + 6x = 27 - x they would get 5 + 7x = 27 (not 5 - 7x). But that equation itself was based on the earlier mistake.
- Steps 4–5: Follow from the earlier mistakes, so the computed x is wrong.

Correct solution:
1. Distribute: 5 + 20x + 2x = 27 - x
2. Combine like terms: 5 + 22x = 27 - x
3. Bring x-terms together: 5 + 23x = 27
4. Subtract 5: 23x = 22
5. x = 22/23

(You can check: substituting x = 22/23 satisfies the original equation.)