Answer :
Sure! Let's solve the equation step-by-step.
The equation given is:
[tex]\[ \frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) \][/tex]
Step 1: Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side of the equation.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4) \][/tex]
Step 2: Simplify the left side by combining like terms.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
[tex]\[ \frac{1}{2}x + 4 = \frac{1}{2}x - x + 4 \][/tex]
Step 3: Simplify the right side by distributing the negative sign and combining like terms.
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]
Step 4: Subtract 4 from both sides to isolate the terms with [tex]\(x\)[/tex].
[tex]\[ \frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \][/tex]
[tex]\[ \frac{1}{2}x = -\frac{1}{2}x \][/tex]
Step 5: Combine like terms by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation.
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \][/tex]
[tex]\[ x = 0 \][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
The equation given is:
[tex]\[ \frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) \][/tex]
Step 1: Distribute the [tex]\(\frac{1}{2}\)[/tex] on the left side of the equation.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x-4) \][/tex]
Step 2: Simplify the left side by combining like terms.
[tex]\[ \frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \][/tex]
[tex]\[ \frac{1}{2}x + 4 = \frac{1}{2}x - x + 4 \][/tex]
Step 3: Simplify the right side by distributing the negative sign and combining like terms.
[tex]\[ \frac{1}{2}x + 4 = -\frac{1}{2}x + 4 \][/tex]
Step 4: Subtract 4 from both sides to isolate the terms with [tex]\(x\)[/tex].
[tex]\[ \frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4 \][/tex]
[tex]\[ \frac{1}{2}x = -\frac{1}{2}x \][/tex]
Step 5: Combine like terms by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides of the equation.
[tex]\[ \frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x \][/tex]
[tex]\[ x = 0 \][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
