Answer :
Sure! Let's solve the equation step-by-step:
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we'll simplify both sides of the equation.
1. Distribute on the left side:
[tex]\[
\frac{1}{2} \times (x - 14) = \frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
2. Simplify on the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now our equation is simplified to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant part:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] from the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine the [tex]\(x\)[/tex] terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
We start with the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
First, we'll simplify both sides of the equation.
1. Distribute on the left side:
[tex]\[
\frac{1}{2} \times (x - 14) = \frac{1}{2}x - \frac{1}{2} \times 14 = \frac{1}{2}x - 7
\][/tex]
So, the left side becomes:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4
\][/tex]
2. Simplify on the right side:
[tex]\[
\frac{1}{2}x - (x - 4) = \frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4
\][/tex]
Now our equation is simplified to:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides to eliminate the constant part:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(-\frac{1}{2}x\)[/tex] from the right side:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine the [tex]\(x\)[/tex] terms on the left side:
[tex]\[
x = 0
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
