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Solve for [tex] x [/tex]:

[tex] \frac{x}{-4} \geq -25 [/tex]

A) [tex] x \geq 100 [/tex]
B) [tex] x \geq -100 [/tex]
C) [tex] x \leq 100 [/tex]
D) [tex] x \leq -100 [/tex]

Answer :

To solve the inequality [tex]\(\frac{x}{-4} \geq -25\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here are the step-by-step instructions:

1. Start with the inequality:
[tex]\[
\frac{x}{-4} \geq -25
\][/tex]

2. To eliminate the fraction, multiply both sides of the inequality by [tex]\(-4\)[/tex]. Remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality sign:
[tex]\[
x \leq -25 \times (-4)
\][/tex]

3. Calculate [tex]\(-25 \times (-4)\)[/tex]:
[tex]\[
-25 \times (-4) = 100
\][/tex]

4. Substitute this result back into the inequality:
[tex]\[
x \leq 100
\][/tex]

Therefore, the solution to the inequality is:
[tex]\[
x \leq 100
\][/tex]

The correct answer is option C) [tex]\(x \leq 100\)[/tex].

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