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Answer :
Sure, let's work through the equation step-by-step to find the value of [tex]\( x \)[/tex].
We start with the equation Karissa was solving:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides.
- Distribute on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
So the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify the constants:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
-(x-4) = -x + 4
\][/tex]
Substituting it back, the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Step 2: Set them equal (as shown after simplification in the solution):
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Combine like terms by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
We start with the equation Karissa was solving:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
Step 1: Simplify both sides.
- Distribute on the left side:
[tex]\[
\frac{1}{2}(x-14) = \frac{1}{2}x - 7
\][/tex]
So the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11
\][/tex]
Simplify the constants:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
- On the right side, distribute the negative sign:
[tex]\[
-(x-4) = -x + 4
\][/tex]
Substituting it back, the right side becomes:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Step 2: Set them equal (as shown after simplification in the solution):
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Combine like terms by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the negative term:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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