Find the exact step where a solution goes wrong, say what the mistake is, and correct it.
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Five mistakes to watch for.
Check each line: was the same thing done to both sides?
For each pair of lines, ask: what operation turned this line into the next? Was it done to the whole of both sides?
The book's first three solutions, checked line by line.
Problem. Decide whether each solution is correct. If not, describe the mistake and correct it. (Textbook p. 181, items 1–3)
Find, explain and correct the mistakes in six solutions.
Textbook pp. 181–182, items 4–9. For each solution, find the wrong line, say what went wrong, and give the correct answer.
4. 5z + 2 = 3z − 4 → 5z + 3z = −4 + 2 → 8z = −2 → z = −2/8
5. 15w − 4w = 26 → 15w = 26 + 4w → 15w = 30 → w = 2
6. 3x + 1 = −12 → x + 1 = −12/3 → x + 1 = −4 → x = −5
7. 4(4q + 2) = 50 → 4(4q) = 50 − 2 → 16q = 48 → q = 3
8. −2(3 − 4x) = 14 → −6v − 8x = 14 → −8x = 14 + 6 → −8x = 20 → x = −20/8
9. 3(7y + 4) = 9 + 5y → 7y + 4 = 9/3 + 5y → 7y + 4 = 3 + 5y → 7y − 5y + 4 = 3 → 2y = 4 − 3 → y = 1/2
Judge three more solutions.
6x + 9 = 66 → x + 9 = 11 → x = 2. (p. 187, Q11a) What is the correct answer?