en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

| 3/(5-2x)|<= 2

Solution

\frac{3}{5 - 2 x} \leq 2

Solution

x \leq \frac{7}{4} or x \geq \frac{13}{4}

+2

Interval Notation

(- \infty, \frac{7}{4}] \cup [\frac{13}{4}, \infty)

Decimal Notation

x \leq 1.75 or x \geq 3.25

Solution steps

\frac{3}{5 - 2 x} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{3}{5 - 2 x} \leq 2

\frac{3}{5 - 2 x} \geq - 2 and \frac{3}{5 - 2 x} \leq 2

(x < \frac{5}{2} or x \geq \frac{13}{4}) and (x \leq \frac{7}{4} or x > \frac{5}{2})

Merge Overlapping Intervals

x \leq \frac{7}{4} or x \geq \frac{13}{4}

Popular Examples

x + 4 = - 3

6 x^{2} - 48 = - 12 x

x^{2} - 4 x + 40 = 0

5 x^{2} + 6 x + 3 \geq 0

x^{2} + 12 x + 15 = 0

Frequently Asked Questions (FAQ)

What is | 3/(5-2x)|<= 2 ?
The solution to | 3/(5-2x)|<= 2 is x<= 7/4 \lor x>= 13/4