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Solve the compound inequality below:

[tex]\[ x - 2 \ \textless \ -11 \text{ or } -3x \leq -18 \][/tex]

A. [tex]\( x \ \textless \ -9 \)[/tex] or [tex]\( x \geq 6 \)[/tex]

B. [tex]\(-9 \ \textgreater \ x \geq 6 \)[/tex]

C. [tex]\( x \ \textless \ -13 \)[/tex] or [tex]\( x \geq -6 \)[/tex]

D. [tex]\(-13 \ \textless \ x \ \textgreater \ -6\)[/tex]


Sagot :

To solve the compound inequality [tex]\(x - 2 < -11\)[/tex] or [tex]\(-3x \leq -18\)[/tex], let's solve each part step-by-step:

### Part 1: [tex]\(x - 2 < -11\)[/tex]

1. Start with the inequality:
[tex]\[ x - 2 < -11 \][/tex]

2. Add 2 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x - 2 + 2 < -11 + 2 \][/tex]
[tex]\[ x < -9 \][/tex]

### Part 2: [tex]\(-3x \leq -18\)[/tex]

1. Start with the inequality:
[tex]\[ -3x \leq -18 \][/tex]

2. Divide both sides by -3. Remember to reverse the inequality symbol when dividing by a negative number:
[tex]\[ x \geq \frac{-18}{-3} \][/tex]
[tex]\[ x \geq 6 \][/tex]

### Combining the Inequalities

Now that we have solved each individual inequality, we combine the results. The solution to the original compound inequality [tex]\(x - 2 < -11\)[/tex] or [tex]\(-3x \leq -18\)[/tex] is:
[tex]\[ x < -9 \quad \text{or} \quad x \geq 6 \][/tex]

So, the final solution is:
[tex]\[ x < -9 \quad \text{or} \quad x \geq 6 \][/tex]

This means that [tex]\(x\)[/tex] can be any number less than -9 or any number greater than or equal to 6.