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Answer :
Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
The original equation is:
[tex]\[ \frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4) \][/tex]
First, we'll simplify both sides:
1. Expand [tex]\(\frac{1}{2}(x-14)\)[/tex]:
[tex]\[ \frac{1}{2} x - \frac{1}{2} \cdot 14 = \frac{1}{2} x - 7 \][/tex]
2. Simplify the expression [tex]\(- (x-4)\)[/tex]:
[tex]\[ -(x-4) = -x + 4 \][/tex]
Now substitute these into the equation:
[tex]\[ \frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4 \][/tex]
3. Combine like terms on both sides:
- Left side:
[tex]\[ \frac{1}{2} x + 4 \][/tex]
- Right side:
[tex]\[ \frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4 \][/tex]
Now the equation looks like this:
[tex]\[ \frac{1}{2} x + 4 = -\frac{1}{2} x + 4 \][/tex]
4. Subtract 4 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[ \frac{1}{2} x = -\frac{1}{2} x \][/tex]
5. Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to combine like terms:
[tex]\[ \frac{1}{2} x + \frac{1}{2} x = 0 \][/tex]
6. Simplify:
[tex]\[ x = 0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
The original equation is:
[tex]\[ \frac{1}{2}(x-14) + 11 = \frac{1}{2} x - (x-4) \][/tex]
First, we'll simplify both sides:
1. Expand [tex]\(\frac{1}{2}(x-14)\)[/tex]:
[tex]\[ \frac{1}{2} x - \frac{1}{2} \cdot 14 = \frac{1}{2} x - 7 \][/tex]
2. Simplify the expression [tex]\(- (x-4)\)[/tex]:
[tex]\[ -(x-4) = -x + 4 \][/tex]
Now substitute these into the equation:
[tex]\[ \frac{1}{2} x - 7 + 11 = \frac{1}{2} x - x + 4 \][/tex]
3. Combine like terms on both sides:
- Left side:
[tex]\[ \frac{1}{2} x + 4 \][/tex]
- Right side:
[tex]\[ \frac{1}{2} x - x + 4 = -\frac{1}{2} x + 4 \][/tex]
Now the equation looks like this:
[tex]\[ \frac{1}{2} x + 4 = -\frac{1}{2} x + 4 \][/tex]
4. Subtract 4 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[ \frac{1}{2} x = -\frac{1}{2} x \][/tex]
5. Add [tex]\(\frac{1}{2} x\)[/tex] to both sides to combine like terms:
[tex]\[ \frac{1}{2} x + \frac{1}{2} x = 0 \][/tex]
6. Simplify:
[tex]\[ x = 0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
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