Let's solve the given inequality step-by-step:
[tex]\[
\frac{1}{2} - \frac{1}{4}x \geq -\frac{1}{4}
\][/tex]
### Step 1: Eliminate Fractions
Multiply every term by 4 to eliminate the fractions. This gives:
[tex]\[
4 \left( \frac{1}{2} \right) - 4 \left( \frac{1}{4} x \right) \geq 4 \left( -\frac{1}{4} \right)
\][/tex]
[tex]\[
2 - x \geq -1
\][/tex]
### Step 2: Isolate the Variable
Add [tex]\( x \)[/tex] to both sides to isolate [tex]\( x \)[/tex] on one side:
[tex]\[
2 \geq -1 + x
\][/tex]
### Step 3: Simplify
Add 1 to both sides to further isolate [tex]\( x \)[/tex]:
[tex]\[
2 + 1 \geq x
\][/tex]
[tex]\[
3 \geq x
\][/tex]
Which can be rewritten as:
[tex]\[
x \leq 3
\][/tex]
### Solution:
The solution to the inequality [tex]\(\frac{1}{2} - \frac{1}{4}x \geq -\frac{1}{4}\)[/tex] is:
[tex]\[
x \leq 3
\][/tex]
In interval notation, this is:
[tex]\[
(-\infty, 3]
\][/tex]
So, among the given choices:
- [tex]\( x \leq 3 \)[/tex] is the correct solution.
