Question

which step contains the first error in solving the equation |3x - 7| + 13 = 18, and what should have been done instead? step 1: |3x - 7| + 13 = 18 step 2: |3x - 7| = 5 step 3: consider the positive case, 3x - 7 = 5 step 4: 3x = -12 step 5: x = -4 step 6: |3x - 7| = 5 step 7: consider the negative case, 3x - 7 = -5 step 8: 3x = 2 step 9: x = 2/3 step 10: the solutions to the equation are -4 or 2/3. step 9; it should have been x = step 2; it should have been |3x - 7| = 15 step 4; it should have been 3x = 12 step 7; it should have been -3x - 7 = 5

Explanation:

Step1: Analyze original equation start

Original equation: $|3x - 7| + 13 = 18$

Step2: Check Step 2 isolation

Subtract 13: $|3x - 7| = 18 - 13 = 5$, Step2 is correct.

Step3: Check positive case Step4

Positive case: $3x - 7 = 5$. Add 7: $3x = 5 + 7 = 12$. Step4 incorrectly wrote $3x=-12$.

Step4: Verify other steps for errors

Step7 negative case: $3x - 7 = -5$ is correct (negative case flips the right-hand side, not the left). Step9 calculation is correct for its equation.

Answer:

Step 4; it should have been $3x = 12$