Answer :
Sure! Let's solve the equation step-by-step to find the value of [tex]\(x\)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Expand both sides of the equation.
Left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex] inside the parentheses: [tex]\(\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11\)[/tex]
Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
- Distribute the negative sign: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
Now the equation looks like this:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Simplify both sides.
Left side: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
Right side: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex]
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides to eliminate the constant term.
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms.
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Which simplifies to:
[tex]\[
x = 0
\][/tex]
So the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x - 14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Expand both sides of the equation.
Left side: [tex]\(\frac{1}{2}(x - 14) + 11\)[/tex]
- Distribute [tex]\(\frac{1}{2}\)[/tex] inside the parentheses: [tex]\(\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11\)[/tex]
Right side: [tex]\(\frac{1}{2}x - (x - 4)\)[/tex]
- Distribute the negative sign: [tex]\(\frac{1}{2}x - x + 4\)[/tex]
Now the equation looks like this:
[tex]\[
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4
\][/tex]
Step 2: Simplify both sides.
Left side: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4\)[/tex]
Right side: [tex]\(\frac{1}{2}x - x + 4 = -\frac{1}{2}x + 4\)[/tex]
Now the equation is:
[tex]\[
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\][/tex]
Step 3: Subtract 4 from both sides to eliminate the constant term.
[tex]\[
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms.
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x
\][/tex]
Which simplifies to:
[tex]\[
x = 0
\][/tex]
So the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
