en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1+|x-3/2 |>= 2

Solution

1 + x - \frac{3}{2} \geq 2

Solution

x \leq \frac{1}{2} or x \geq \frac{5}{2}

+2

Interval Notation

(- \infty, \frac{1}{2}] \cup [\frac{5}{2}, \infty)

Decimal Notation

x \leq 0.5 or x \geq 2.5

Solution steps

1 + x - \frac{3}{2} \geq 2

Move

1

to the right side

x - \frac{3}{2} \geq 1

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

x - \frac{3}{2} \leq - 1 or x - \frac{3}{2} \geq 1

x - \frac{3}{2} \leq - 1 or x - \frac{3}{2} \geq 1

x \leq \frac{1}{2} or x \geq \frac{5}{2}

Popular Examples

(x-3)/(x+3)<= 2

\frac{x - 3}{x + 3} \leq 2

4 - 4 x \geq 9

- 2 (x - 5) = - 16

2 < 4

simplify log_{5}(1/625)simplify

lo g_{5} (\frac{1}{625})

Frequently Asked Questions (FAQ)

What is 1+|x-3/2 |>= 2 ?
The solution to 1+|x-3/2 |>= 2 is x<= 1/2 \lor x>= 5/2