To solve the compound inequality [tex]\(5x - 7 \geq 8\)[/tex] or [tex]\(4x + 4 < -20\)[/tex], we need to solve each inequality separately and then combine the solutions using the logical "or."
### Step 1: Solve [tex]\(5x - 7 \geq 8\)[/tex]
1. Isolate [tex]\(x\)[/tex]:
[tex]\[
5x - 7 \geq 8
\][/tex]
2. Add 7 to both sides:
[tex]\[
5x \geq 15
\][/tex]
3. Divide both sides by 5:
[tex]\[
x \geq 3
\][/tex]
### Step 2: Solve [tex]\(4x + 4 < -20\)[/tex]
1. Isolate [tex]\(x\)[/tex]:
[tex]\[
4x + 4 < -20
\][/tex]
2. Subtract 4 from both sides:
[tex]\[
4x < -24
\][/tex]
3. Divide both sides by 4:
[tex]\[
x < -6
\][/tex]
### Step 3: Combine the solutions
The solutions to the inequalities are:
1. [tex]\(x \geq 3\)[/tex] from the first inequality.
2. [tex]\(x < -6\)[/tex] from the second inequality.
Combining these, we get [tex]\(x \geq 3\)[/tex] or [tex]\(x < -6\)[/tex].
Thus, the correct answer is:
a. [tex]\(x \geq 3\)[/tex] or [tex]\(x < -6\)[/tex].
