Question

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

Answer 1

`\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}`