Answer :
Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
Given the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the terms on both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. To isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is 0.
Given the equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4)
\][/tex]
1. Distribute the terms on both sides:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
2. Simplify both sides:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
3. Subtract 4 from both sides:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
4. To isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
5. Combine like terms:
[tex]\[
x = 0
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is 0.
