Answer :
To solve the inequality [tex]\(\frac{x}{-5} \leq -2\)[/tex], we begin by isolating [tex]\(x\)[/tex]. Here are the steps:
1. Multiply both sides by -5: When multiplying or dividing by a negative number in an inequality, the direction of the inequality changes. So, we multiply both sides of the inequality [tex]\(\frac{x}{-5} \leq -2\)[/tex] by -5:
[tex]\[ x \geq (-2) \times (-5) \][/tex]
2. Simplify:
[tex]\[ x \geq 10 \][/tex]
This means that [tex]\(x\)[/tex] should be greater than or equal to 10 to satisfy the inequality.
Now, let's evaluate the given options to see which ones satisfy [tex]\(x \geq 10\)[/tex]:
A. [tex]\(1\)[/tex]
[tex]\[ 1 \not\geq 10 \][/tex]
This does not satisfy the inequality.
B. [tex]\(0\)[/tex]
[tex]\[ 0 \not\geq 10 \][/tex]
This does not satisfy the inequality.
C. [tex]\(25\)[/tex]
[tex]\[ 25 \geq 10 \][/tex]
This does satisfy the inequality.
D. [tex]\(-5\)[/tex]
[tex]\[ -5 \not\geq 10 \][/tex]
This does not satisfy the inequality.
E. [tex]\(18\)[/tex]
[tex]\[ 18 \geq 10 \][/tex]
This does satisfy the inequality.
F. [tex]\(10\)[/tex]
[tex]\[ 10 \geq 10 \][/tex]
This does satisfy the inequality.
Therefore, the correct answers that are in the solution set of the inequality [tex]\(\frac{x}{-5} \leq -2\)[/tex] are:
- 25 (Option C)
- 18 (Option E)
- 10 (Option F)
1. Multiply both sides by -5: When multiplying or dividing by a negative number in an inequality, the direction of the inequality changes. So, we multiply both sides of the inequality [tex]\(\frac{x}{-5} \leq -2\)[/tex] by -5:
[tex]\[ x \geq (-2) \times (-5) \][/tex]
2. Simplify:
[tex]\[ x \geq 10 \][/tex]
This means that [tex]\(x\)[/tex] should be greater than or equal to 10 to satisfy the inequality.
Now, let's evaluate the given options to see which ones satisfy [tex]\(x \geq 10\)[/tex]:
A. [tex]\(1\)[/tex]
[tex]\[ 1 \not\geq 10 \][/tex]
This does not satisfy the inequality.
B. [tex]\(0\)[/tex]
[tex]\[ 0 \not\geq 10 \][/tex]
This does not satisfy the inequality.
C. [tex]\(25\)[/tex]
[tex]\[ 25 \geq 10 \][/tex]
This does satisfy the inequality.
D. [tex]\(-5\)[/tex]
[tex]\[ -5 \not\geq 10 \][/tex]
This does not satisfy the inequality.
E. [tex]\(18\)[/tex]
[tex]\[ 18 \geq 10 \][/tex]
This does satisfy the inequality.
F. [tex]\(10\)[/tex]
[tex]\[ 10 \geq 10 \][/tex]
This does satisfy the inequality.
Therefore, the correct answers that are in the solution set of the inequality [tex]\(\frac{x}{-5} \leq -2\)[/tex] are:
- 25 (Option C)
- 18 (Option E)
- 10 (Option F)
