High School

Which values for x make this inequality true?

\(-\frac{1}{5}x + 4 \leq 39\)

A. [tex]x \leq 175[/tex]
B. [tex]x \geq 175[/tex]
C. [tex]x \geq -175[/tex]
D. [tex]x \leq -175[/tex]

Answer :

Final answer:

To solve the inequality -1/5x + 4 ≤ 39, we isolate x and reverse the inequality sign when multiplying by a negative, resulting in x ≥ 175. Thus, the correct answer is b) x ≥ 175.

Explanation:

The student asked which values for x make the inequality -1/5x + 4 ≤ 39 true. To solve for x, we first move the constant term to the right side of the inequality:

-1/5x ≤ 39 - 4

-1/5x ≤ 35

Now, multiply both sides by -5 to solve for x. Remember, multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality.

x ≥ -35 × -5

x ≥ 175

Therefore, the correct answer is b) x ≥ 175.

Learn more about Solving Inequalities here:

https://brainly.com/question/26855203

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