Answer :
We start with the equation:
[tex]$$
-\frac{1}{2}x + 4 = x + 1.
$$[/tex]
Step 1: Eliminate the Fraction
Multiply both sides of the equation by 2 to remove the fraction:
[tex]$$
2\left(-\frac{1}{2}x + 4\right) = 2(x + 1).
$$[/tex]
This simplifies to:
[tex]$$
-x + 8 = 2x + 2.
$$[/tex]
Step 2: Get the [tex]$x$[/tex] Terms Together
Add [tex]$x$[/tex] to both sides to gather the [tex]$x$[/tex] terms on the right side:
[tex]$$
-x + x + 8 = 2x + x + 2,
$$[/tex]
which simplifies to:
[tex]$$
8 = 3x + 2.
$$[/tex]
Step 3: Isolate the [tex]$x$[/tex] Term
Subtract 2 from both sides to isolate the term containing [tex]$x$[/tex]:
[tex]$$
8 - 2 = 3x,
$$[/tex]
so we have:
[tex]$$
6 = 3x.
$$[/tex]
Step 4: Solve for [tex]$x$[/tex]
Finally, divide both sides by 3:
[tex]$$
\frac{6}{3} = x,
$$[/tex]
which simplifies to:
[tex]$$
x = 2.
$$[/tex]
Thus, the solution to the equation is [tex]$\boxed{2}$[/tex].
[tex]$$
-\frac{1}{2}x + 4 = x + 1.
$$[/tex]
Step 1: Eliminate the Fraction
Multiply both sides of the equation by 2 to remove the fraction:
[tex]$$
2\left(-\frac{1}{2}x + 4\right) = 2(x + 1).
$$[/tex]
This simplifies to:
[tex]$$
-x + 8 = 2x + 2.
$$[/tex]
Step 2: Get the [tex]$x$[/tex] Terms Together
Add [tex]$x$[/tex] to both sides to gather the [tex]$x$[/tex] terms on the right side:
[tex]$$
-x + x + 8 = 2x + x + 2,
$$[/tex]
which simplifies to:
[tex]$$
8 = 3x + 2.
$$[/tex]
Step 3: Isolate the [tex]$x$[/tex] Term
Subtract 2 from both sides to isolate the term containing [tex]$x$[/tex]:
[tex]$$
8 - 2 = 3x,
$$[/tex]
so we have:
[tex]$$
6 = 3x.
$$[/tex]
Step 4: Solve for [tex]$x$[/tex]
Finally, divide both sides by 3:
[tex]$$
\frac{6}{3} = x,
$$[/tex]
which simplifies to:
[tex]$$
x = 2.
$$[/tex]
Thus, the solution to the equation is [tex]$\boxed{2}$[/tex].
