Question

where did dariel make a mistake? step 3 what should dariel do in step 3 instead? multiply by 2 add \\(\frac{1}{2}\\) multiply by \\(\frac{1}{2}\\) add 2 dariels work \\(\frac{1}{2}x + 6 = x + 10\\) step 1 \\(- \frac{1}{2}x\\) \\(- \frac{1}{2}x\\) \\(6 = \frac{1}{2}x + 10\\) step 2 \\(- 10\\) \\(- 10\\) \\(-4 = \frac{1}{2}x\\) step 3 \\(-4 \div 2 = \frac{1}{2}x \div 2\\) \\(-2 = x\\)

Explanation:

Step1: Analyze the equation after Step 2

After Step 2, we have \(-4=\frac{1}{2}x\). To solve for \(x\), we need to isolate \(x\). The coefficient of \(x\) is \(\frac{1}{2}\), so we should multiply both sides by the reciprocal of \(\frac{1}{2}\), which is \(2\).

Step2: Identify the mistake in Step 3

In Step 3, Dariel divided both sides by \(2\), but that's incorrect. Dividing \(\frac{1}{2}x\) by \(2\) gives \(\frac{1}{4}x\), not \(x\). Instead, multiplying both sides by \(2\) will eliminate the fraction. So the correct operation for Step 3 is to multiply both sides by \(2\).

Answer:

Multiply by 2