To determine which values satisfy the inequality [tex]\(-3x - 4 < 2\)[/tex], let's solve it step-by-step:
1. Start with the inequality:
[tex]\[ -3x - 4 < 2 \][/tex]
2. Isolate the term with [tex]\(x\)[/tex]:
- First, add 4 to both sides to get rid of the constant term on the left-hand side.
[tex]\[ -3x - 4 + 4 < 2 + 4 \][/tex]
- This simplifies to:
[tex]\[ -3x < 6 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Next, divide both sides of the inequality by -3. Remember, when you divide by a negative number, you must reverse the inequality sign.
[tex]\[ x > -2 \][/tex]
Hence, the inequality simplifies to:
[tex]\[ x > -2 \][/tex]
Now, let's check each of the given values to see if it satisfies [tex]\(x > -2\)[/tex]:
- For [tex]\(x = -4\)[/tex]:
[tex]\[ -4 > -2 \][/tex]
This is false. So, [tex]\(-4\)[/tex] is not a solution.
- For [tex]\(x = -2\)[/tex]:
[tex]\[ -2 > -2 \][/tex]
This is false. So, [tex]\(-2\)[/tex] is not a solution.
- For [tex]\(x = 0\)[/tex]:
[tex]\[ 0 > -2 \][/tex]
This is true. So, [tex]\(0\)[/tex] is a solution.
- For [tex]\(x = 3\)[/tex]:
[tex]\[ 3 > -2 \][/tex]
This is true. So, [tex]\(3\)[/tex] is a solution.
The values that satisfy [tex]\(x > -2\)[/tex] are [tex]\(0\)[/tex] and [tex]\(3\)[/tex]. Therefore, the correct values are:
- [tex]\(0\)[/tex]
- [tex]\(3\)[/tex]
Please check these values from the given options.
