Let's solve the inequality step by step:
1. Distribute the [tex]\(-\frac{1}{4}\)[/tex] on the left side of the inequality:
[tex]\[
-\frac{1}{4}(12x + 8) = -3x - 2
\][/tex]
So, the inequality becomes:
[tex]\[
-3x - 2 \leq -2x + 11
\][/tex]
2. Isolate [tex]\(x\)[/tex] by adding [tex]\(3x\)[/tex] to both sides:
[tex]\[
-3x - 2 + 3x \leq -2x + 3x + 11
\][/tex]
Simplifying this, we get:
[tex]\[
-2 \leq x + 11
\][/tex]
3. Subtract [tex]\(11\)[/tex] from both sides:
[tex]\[
-2 - 11 \leq x
\][/tex]
Simplifying this, we get:
[tex]\[
-13 \leq x
\][/tex]
Which is equivalent to:
[tex]\[
x \geq -13
\][/tex]
4. Interpreting the result:
The solution to the inequality is [tex]\( x \geq -13 \)[/tex]. This means that the values of [tex]\( x \)[/tex] are all numbers greater than or equal to [tex]\(-13\)[/tex].
To find the graph that represents this solution:
- The graph will show a number line.
- There should be a closed circle at [tex]\( -13 \)[/tex] indicating that [tex]\(-13\)[/tex] is included in the solution.
- The line should extend to the right from [tex]\(-13\)[/tex], indicating all numbers greater than or equal to [tex]\(-13\)[/tex].
Compare the graphs given in options A, B, C, and D to find the one that matches this description.
Since the solution tells us [tex]\( x \geq -13\)[/tex], the correct graph will be the one that displays all values of [tex]\( x \)[/tex] greater than or equal to [tex]\(-13\)[/tex] with a closed circle at [tex]\(-13\)[/tex].
