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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 and simplify both sides of the equation.
On the left side, distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify [tex]\(-7 + 11\)[/tex] to get:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign in front of [tex]\((x - 4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Step 2: Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 3: Simplify the equation further.
Start by eliminating the constant 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Solve for [tex]\( x \)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get rid of the [tex]\( -\frac{1}{2}x \)[/tex] on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This combines to:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\( x = 0 \)[/tex].
We start with the given equation:
[tex]\[
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x - 4)
\][/tex]
Step 1: Expand and simplify both sides of the equation.
On the left side, distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2}x - \frac{1}{2} \times 14 + 11 = \frac{1}{2}x - 7 + 11
\][/tex]
Simplify [tex]\(-7 + 11\)[/tex] to get:
[tex]\[
\frac{1}{2}x + 4
\][/tex]
On the right side, distribute the negative sign in front of [tex]\((x - 4)\)[/tex]:
[tex]\[
\frac{1}{2}x - x + 4
\][/tex]
Step 2: Set the simplified expressions equal to each other:
[tex]\[
\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4
\][/tex]
Step 3: Simplify the equation further.
Start by eliminating the constant 4 from both sides of the equation:
[tex]\[
\frac{1}{2}x = \frac{1}{2}x - x
\][/tex]
Simplify the right side:
[tex]\[
\frac{1}{2}x = -\frac{1}{2}x
\][/tex]
Step 4: Solve for [tex]\( x \)[/tex].
Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to get rid of the [tex]\( -\frac{1}{2}x \)[/tex] on the right:
[tex]\[
\frac{1}{2}x + \frac{1}{2}x = 0
\][/tex]
This combines to:
[tex]\[
x = 0
\][/tex]
So, the solution to the equation is [tex]\( x = 0 \)[/tex].
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Rewritten by : Barada
