Let's solve the equation step-by-step as Karissa did to find the value of [tex]\( x \)[/tex].
Given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2} x - (x - 4)
\][/tex]
First, we distribute [tex]\(\frac{1}{2}\)[/tex] on the left side:
[tex]\[
\frac{1}{2}x - \frac{1}{2}(14) + 11 = \frac{1}{2}x - x + 4
\][/tex]
Simplify the left side:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Combine like terms on the left side:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Notice that both sides of the equation have a [tex]\(4\)[/tex]. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
To solve [tex]\(\frac{1}{2}x = -\frac{1}{2}\)[/tex], we add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2} + \frac{1}{2}x
\][/tex]
Combine like terms:
[tex]\[
x = -1
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( -1 \)[/tex].
