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Answer :
Sure! Let's solve the equation step-by-step using Karissa's work as a guide:
We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Expand and simplify both sides.
First, distribute on both sides:
Left Side:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Right Side:
Subtract:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So the simplified equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
To isolate the [tex]\(x\)[/tex] terms, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 0.
We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Expand and simplify both sides.
First, distribute on both sides:
Left Side:
[tex]\[
\frac{1}{2} \cdot x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
Right Side:
Subtract:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
\][/tex]
Simplify:
[tex]\[
-\frac{1}{2}x + 4
\][/tex]
So the simplified equation becomes:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 2: Subtract 4 from both sides.
To isolate the [tex]\(x\)[/tex] terms, subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This simplifies to:
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 0.
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