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Answer :
Sure! Let's solve the equation step-by-step:
The equation Karissa is working with is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
### Step 1: Simplify Each Side
First, simplify both sides of the equation.
On the left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
= -\frac{1}{2}x + 4
\][/tex]
### Step 2: Set the Simplified Equation
Now, set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
### Step 3: Isolate [tex]\(x\)[/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Next, add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
### Conclusion
The value of [tex]\(x\)[/tex] is 0.
The equation Karissa is working with is:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
### Step 1: Simplify Each Side
First, simplify both sides of the equation.
On the left side:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - \frac{1}{2} \cdot 14 + 11 = \frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
On the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4
= -\frac{1}{2}x + 4
\][/tex]
### Step 2: Set the Simplified Equation
Now, set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
### Step 3: Isolate [tex]\(x\)[/tex]
Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Next, add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get all the [tex]\(x\)[/tex] terms on one side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
Combine like terms:
[tex]\[
x = 0
\][/tex]
### Conclusion
The value of [tex]\(x\)[/tex] is 0.
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