Certainly! Let's solve the given inequalities step-by-step.
### First Inequality: [tex]\(-\frac{1}{3}x - 12 > 21\)[/tex]
1. Isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-\frac{1}{3}x - 12 > 21
\][/tex]
Add 12 to both sides:
[tex]\[
-\frac{1}{3}x > 33
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Multiply both sides by [tex]\(-3\)[/tex], and remember to flip the inequality sign when multiplying by a negative number:
[tex]\[
x < -99
\][/tex]
So, the first inequality solution is:
[tex]\[
x < -99
\][/tex]
### Second Inequality: [tex]\(-6x + 10 < -2\)[/tex]
1. Isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-6x + 10 < -2
\][/tex]
Subtract 10 from both sides:
[tex]\[
-6x < -12
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-6\)[/tex], and remember to flip the inequality sign when dividing by a negative number:
[tex]\[
x > 2
\][/tex]
So, the second inequality solution is:
[tex]\[
x > 2
\][/tex]
### Combined Solution
The combined solution for the inequalities is:
[tex]\[
x < -99 \quad \text{or} \quad x > 2
\][/tex]
