Question

karissa begins to solve the equation (\frac{1}{2}(x - 14)+11=\frac{1}{2}x-(x - 4)). her work is correct and is shown below. (\frac{1}{2}(x - 14)+11=\frac{1}{2}x-(x - 4)) (\frac{1}{2}x - 7 + 11=\frac{1}{2}x - x + 4) (\frac{1}{2}x + 4=-\frac{1}{2}x + 4) when she subtracts 4 from both sides, results. what is the value of (x)? (\bigcirc -1) (\bigcirc \frac{1}{2}) (\bigcirc 0) (\bigcirc \frac{1}{2})

Explanation:

Step1: Subtract 4 from both sides

We have the equation $\frac{1}{2}x + 4=-\frac{1}{2}x + 4$. Subtract 4 from both sides:
$\frac{1}{2}x+4 - 4=-\frac{1}{2}x + 4-4$
Simplify to get $\frac{1}{2}x=-\frac{1}{2}x$

Step2: Add $\frac{1}{2}x$ to both sides

Add $\frac{1}{2}x$ to both sides of $\frac{1}{2}x=-\frac{1}{2}x$:
$\frac{1}{2}x+\frac{1}{2}x=-\frac{1}{2}x+\frac{1}{2}x$
Simplify the left side: $\frac{1 + 1}{2}x=\frac{2}{2}x=x$
Simplify the right side: $0$
So we have $x = 0$

Answer:

$0$ (corresponding to the option "0")