Question

What's the solution set of –4x + 1 ≤ 9 or x∕5 + 2 < 3?

Question 3 options:

A)

All real numbers

B)

x ≥ –2 or x < 5

C)

2 ≤ x < 5

D)

There is no solution.

Answer 1

B) is your answer x>_-2 or x<5

Answer 2

B) x ≥ –2 or x < 5

Explanation:

We can immediately rule out A) All real numbers, since that will almost never be true for an inequality like this. We can also rule out C) 2 ≤ x < 5, since this is not a compound inequality.

Let's see if B) x ≥ –2 or x < 5 works by plugging in an x value greater than -2 and then, plugging in an x value less than 5.

Plug -1 into x

–4(-1) + 1 ≤ 9

4 + 1 ≤ 9

Combine like terms

5 ≤ 9

This is true, 5 is less than 9, so x ≥ –2 works.

Plug 4 into x

4∕5 + 2 < 3

Combine like terms

2.8 < 3

This is true, 2.8 is less than 3.

It can't be D) no solution now that B works, so B) x ≥ –2 or x < 5 is your answer.

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