Express x ⩽ −5 or x ⩾ −1 in the form ∣x+a∣ ⩾ b

Question

asked May 28, 2021 143k views

1 Answer

Astaar · Answer 1 · 2021-06-01T09:29:05+0000

Answer:

$\mid x+3\mid\ge 2$

Explanation:

Inequalities

The solution for the inequality:

$\mid x+a\mid\ge b$

Can be expressed as:

$x+a\ge b$

OR:

$x+a\le -b$

Subtracting a to both inequalities:

$x\ge b-a$

$x\le -b-a$

Comparing to the given solutions, we have:

b-a=-1

-b-a=-5

Adding both equations:

-2a=-6

Solving:

a=3

b=2

Thus, the required inequality form is:

$\mathbf{\mid x+3\mid\ge 2}$