Answer :
Sure! Let's go through the solution step-by-step to find the value of [tex]\( x \)[/tex] in the equation:
Karissa's work starts with:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Her first step simplifies the equation:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] through [tex]\((x - 14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
2. Simplify the right side by distributing the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
After simplifying, the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, she subtracts 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Now we need to solve for [tex]\( x \)[/tex].
3. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
4. Simplify the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Karissa's work starts with:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Her first step simplifies the equation:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] through [tex]\((x - 14)\)[/tex]:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
2. Simplify the right side by distributing the negative sign:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
After simplifying, the equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Next, she subtracts 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Now we need to solve for [tex]\( x \)[/tex].
3. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation to combine like terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
4. Simplify the left side:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
