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Answer :
Sure! Let's solve the given equation step-by-step.
The equation we need to solve is:
[tex]\[ \frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4) \][/tex]
First, let's distribute and simplify both sides of the equation.
Step 1: Distribute terms inside the parentheses.
[tex]\[ \frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4) \][/tex]
This simplifies to:
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
Step 2: Combine like terms on both sides.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
Simplify the left side:
[tex]\[ \frac{1}{2}x + 4 = \][/tex]
Simplify the right side:
[tex]\[ \frac{1}{2}x - x + 4 \][/tex]
This gives:
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]
Step 3: Subtract 4 from both sides to further simplify.
[tex]\[ \frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \][/tex]
This results in:
[tex]\[ \frac{1}{2}x = -\frac{1}{2}x \][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate [tex]\(x\)[/tex].
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \][/tex]
This simplifies to:
[tex]\[ x = 0 \][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation is:
[tex]\[ \boxed{0} \][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 0.
The equation we need to solve is:
[tex]\[ \frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4) \][/tex]
First, let's distribute and simplify both sides of the equation.
Step 1: Distribute terms inside the parentheses.
[tex]\[ \frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4) \][/tex]
This simplifies to:
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
Step 2: Combine like terms on both sides.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
Simplify the left side:
[tex]\[ \frac{1}{2}x + 4 = \][/tex]
Simplify the right side:
[tex]\[ \frac{1}{2}x - x + 4 \][/tex]
This gives:
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]
Step 3: Subtract 4 from both sides to further simplify.
[tex]\[ \frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \][/tex]
This results in:
[tex]\[ \frac{1}{2}x = -\frac{1}{2}x \][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to isolate [tex]\(x\)[/tex].
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \][/tex]
This simplifies to:
[tex]\[ x = 0 \][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation is:
[tex]\[ \boxed{0} \][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 0.
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