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Answer :
We start with the equation
[tex]$$
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4).
$$[/tex]
Step 1: Simplify the left side.
Distribute [tex]$\frac{1}{2}$[/tex] in the left expression:
[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]
Then add the 11:
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Step 2: Simplify the right side.
Distribute the negative sign on the right expression:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine like terms for [tex]$x$[/tex]:
[tex]$$
\frac{1}{2}x - x = -\frac{1}{2}x,
$$[/tex]
so the right side becomes
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
Step 3: Set up the simplified equation.
Now the equation is
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 4: Subtract 4 from both sides to eliminate the constant term.
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$[/tex]
which simplifies to
[tex]$$
\frac{1}{2}x = -\frac{1}{2}x.
$$[/tex]
Step 5: Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine the terms containing [tex]$x$[/tex].
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x,
$$[/tex]
simplifying to
[tex]$$
x = 0.
$$[/tex]
Thus, the solution for [tex]$x$[/tex] is
[tex]$$
\boxed{0}.
$$[/tex]
[tex]$$
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4).
$$[/tex]
Step 1: Simplify the left side.
Distribute [tex]$\frac{1}{2}$[/tex] in the left expression:
[tex]$$
\frac{1}{2}(x-14) = \frac{1}{2}x - 7.
$$[/tex]
Then add the 11:
[tex]$$
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x + 4.
$$[/tex]
Step 2: Simplify the right side.
Distribute the negative sign on the right expression:
[tex]$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4.
$$[/tex]
Combine like terms for [tex]$x$[/tex]:
[tex]$$
\frac{1}{2}x - x = -\frac{1}{2}x,
$$[/tex]
so the right side becomes
[tex]$$
-\frac{1}{2}x + 4.
$$[/tex]
Step 3: Set up the simplified equation.
Now the equation is
[tex]$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$[/tex]
Step 4: Subtract 4 from both sides to eliminate the constant term.
[tex]$$
\frac{1}{2}x + 4 - 4 = -\frac{1}{2}x + 4 - 4,
$$[/tex]
which simplifies to
[tex]$$
\frac{1}{2}x = -\frac{1}{2}x.
$$[/tex]
Step 5: Add [tex]$\frac{1}{2}x$[/tex] to both sides to combine the terms containing [tex]$x$[/tex].
[tex]$$
\frac{1}{2}x + \frac{1}{2}x = -\frac{1}{2}x + \frac{1}{2}x,
$$[/tex]
simplifying to
[tex]$$
x = 0.
$$[/tex]
Thus, the solution for [tex]$x$[/tex] is
[tex]$$
\boxed{0}.
$$[/tex]
Thanks for taking the time to read Carissa begins to solve the equation tex frac 1 2 x 14 11 frac 1 2 x x 4 tex Her work is shown below. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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