# solve |2x-1| less than or egual to 3?

### 4 Answers

Relevance

- Wayne DeguManLv 73 months ago
|2x - 1| ≤ 3

so, either 2x - 1 ≤ 3 or -(2x - 1) ≤ 3

i.e. either 2x - 1 ≤ 3 or 2x - 1 ≥ -3

so, 2x ≤ 4 or 2x ≥ -2

i.e. x ≤ 2 or x ≥ -1

Combining, we have:

-1 ≤ x ≤ 2....or [-1, 2] using interval notation

:)>

- Log in to reply to the answers

- PopeLv 73 months ago
Both sides are non-negative, so there is no problem with squaring both.

|2x - 1| ≤ 3

(2x - 1)² ≤ 9

(2x - 1)² - 9 ≤ 0

[(2x - 1) + 3][(2x - 1) - 3] ≤ 0

(2x + 2)(2x - 4) ≤ 0

(x + 1)(x - 2) ≤ 0

-1 ≤ x ≤ 2

- Log in to reply to the answers

- ted sLv 73 months ago
you have 2 | x - 1 / 2| | ≤ 3 ===> | x - 1 / 2 | ≤ 3/2 ===> all reals within 3/2 of 1 / 2 =====> [ -1 , 2 ]

- Log in to reply to the answers

- 3 months ago
x is less than or equal to 2

add the one, then divide the 2 by the 4

- Log in to reply to the answers

Still have questions? Get answers by asking now.