Certainly! To determine which values satisfy the inequality [tex]\(-3x - 4 < 2\)[/tex], let's solve this inequality step-by-step.
1. Start with the given inequality:
[tex]\[
-3x - 4 < 2
\][/tex]
2. Add 4 to both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-3x - 4 + 4 < 2 + 4
\][/tex]
Simplifying this, we get:
[tex]\[
-3x < 6
\][/tex]
3. Divide both sides of the inequality by [tex]\(-3\)[/tex]. Remember, when you divide an inequality by a negative number, you must reverse the inequality sign:
[tex]\[
x > \frac{6}{-3}
\][/tex]
Simplifying this, we get:
[tex]\[
x > -2
\][/tex]
Now we need to check which of the given values satisfy [tex]\(x > -2\)[/tex].
- For [tex]\(-4\)[/tex]:
[tex]\(-4 > -2\)[/tex] is false, so [tex]\(-4\)[/tex] is not a solution.
- For [tex]\(-2\)[/tex]:
[tex]\(-2 > -2\)[/tex] is false, so [tex]\(-2\)[/tex] is not a solution.
- For [tex]\(0\)[/tex]:
[tex]\(0 > -2\)[/tex] is true, so [tex]\(0\)[/tex] is a solution.
- For [tex]\(3\)[/tex]:
[tex]\(3 > -2\)[/tex] is true, so [tex]\(3\)[/tex] is a solution.
Therefore, the values that satisfy the inequality [tex]\(-3x - 4 < 2\)[/tex] are:
[tex]\[ \boxed{0 \text{ and } 3} \][/tex]
