Question

error analysis: this problem contains an error during the solving process. choose the arrow for the step in which the mistake was made.
\\(\frac{3}{4}(x + 12) = 6\\)
\\(\frac{3}{4}x + 9 = 6\\) \\(leftarrow\\) step 1
\\(\frac{3}{4}x = 3\\) \\(leftarrow\\) step 2
\\(x = 4\\) \\(leftarrow\\) step 3

error analysis: this problem contains an error during the solving process. choose the arrow for the step in which the mistake was made.
\\(-2(x + 4) - 3(x + 2) = 26\\)
\\(-2x - 8 - 3x - 6 = 26\\) \\(leftarrow\\) step 1
\\(-x - 14 = 26\\) \\(leftarrow\\) step 2
\\(-x = 40\\) \\(leftarrow\\) step 3
\\(x = -40\\) \\(leftarrow\\) step 4

Explanation:

Problem 18 (Equation: \(\boldsymbol{\frac{3}{4}(x + 12)=6}\))

Step 1: Check Step 1

Using the distributive property \(a(b + c)=ab+ac\), \(\frac{3}{4}(x + 12)=\frac{3}{4}x+\frac{3}{4}\times12=\frac{3}{4}x + 9\). So Step 1 is correct.

Step 2: Check Step 2

Subtract 9 from both sides of \(\frac{3}{4}x + 9 = 6\). We get \(\frac{3}{4}x=6 - 9=- 3\), but the step shows \(\frac{3}{4}x = 3\). So the error is in Step 2.

Step 3: Check Step 3 (if Step 2 was correct)

If \(\frac{3}{4}x = 3\), then \(x = 3\div\frac{3}{4}=4\), but since Step 2 has an error, we focus on the first error step.

Step 1: Check Step 1

Using the distributive property: \(-2(x + 4)=-2x-8\) and \(-3(x + 2)=-3x - 6\). So \(-2x-8-3x - 6 = 26\) is correct. Step 1 is correct.

Step 2: Check Step 2

Combine like terms: \(-2x-3x=-5x\) and \(-8 - 6=-14\). So the left - hand side should be \(-5x-14\), but the step shows \(-x - 14\). So the error is in Step 2.

Step 3: Check Step 3 (if Step 2 was correct)

If \(-x-14 = 26\), then \(-x=26 + 14 = 40\), \(x=-40\). But since Step 2 has an error, we identify Step 2 as the error step.

Step 4: Check Step 4 (if previous steps were correct)

If \(-x = 40\), then \(x=-40\), but since Step 2 has an error, we focus on the first error step.

Answer:

The error occurs in Step 2.

Problem 19 (Equation: \(\boldsymbol{-2(x + 4)-3(x + 2)=26}\))