Question

Solve: - 4x + 1 ≤ 21 and 5x + 2 < 22A. x ≥ -5 and x < 4B. x > -5 and x ≤ 4C. x ≥ -5 or x < 4D. x > -5 or x ≤ 4

Answer 1

A. x ≥ -5 and x < 4

Step-by-step explanation

We have the two inequalities:

- 4x + 1 ≤ 21 and 5x + 2 < 22

Let us solve them separately:

FIRST ONE

-4x + 1 ≤ 21

Collect like terms:

-4x ≤ 21 - 1

-4x ≤ 20

Divide through by -4, the sign changes:

`\begin{gathered} x\ge\text{ }(20)/(-4) \\ x\text{ }\ge\text{ -5} \end{gathered}`

SECOND ONE

5x + 2 < 22

Collect like terms:

5x < 22 - 2

5x < 20

Divide through by 5:

x < 20 / 5

x < 4

The answer is Option A.