Question

lets check dariels solution. first, substitute -2 for x.
\\(\frac{1}{2}x + 6 = x + 10\\)
\\(\frac{1}{2}\left( -2 \
ight) + 6 = -2 + 10\\)
is \\(x = -2\\) a solution of the equation?
no
where did dariel make a mistake?
step 1 step 2 step 3
dariel’s 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 Step 1

In Step 1, subtracting \(\frac{1}{2}x\) from both sides of \(\frac{1}{2}x + 6=x + 10\) is correct. The left - hand side becomes \(6\) and the right - hand side becomes \(x-\frac{1}{2}x + 10=\frac{1}{2}x+10\), so Step 1 is correct.

Step2: Analyze Step 2

In Step 2, subtracting 10 from both sides of \(6=\frac{1}{2}x + 10\) gives \(6 - 10=\frac{1}{2}x+10 - 10\), which simplifies to \(- 4=\frac{1}{2}x\), so Step 2 is correct.

Step3: Analyze Step 3

To solve for \(x\) when \(-4=\frac{1}{2}x\), we should multiply both sides by 2 (or divide both sides by \(\frac{1}{2}\)). The correct operation is \(-4\times2=\frac{1}{2}x\times2\) (or \(-4\div\frac{1}{2}=\frac{1}{2}x\div\frac{1}{2}\)). But Dariel divided both sides by 2, which is incorrect. The correct way is to multiply both sides by 2 to isolate \(x\). If we do that, from \(-4=\frac{1}{2}x\), multiplying both sides by 2 gives \(x=-8\), not \(x = - 2\). So the mistake is in Step 3.

Answer:

Step 3