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Which values are solutions to the inequality [tex]-3x - 4 \ \textless \ 2[/tex]? Check all that apply.

A. [tex]-4[/tex]
B. [tex]-2[/tex]
C. [tex]0[/tex]
D. [tex]3[/tex]

Sagot :

GinnyAnswer
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]
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