What is |((3X-5))/(X-1)|>= 1/2 ?

The solution to |((3X-5))/(X-1)|>= 1/2 is X = 9/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|((3X-5))/(X-1)|>= 1/2

\frac{( 3 X - 5 )}{X - 1} \geq \frac{1}{2}

X < 1 or 1 < X \leq \frac{11}{7} or X \geq \frac{9}{5}

Interval Notation

(- \infty, 1) \cup (1, \frac{11}{7}] \cup [\frac{9}{5}, \infty)

Decimal Notation

X < 1 or 1 < X \leq 1.57142 \dots or X \geq 1.8

Solution steps

\frac{3 X - 5}{X - 1} \geq \frac{1}{2}

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{3 X - 5}{X - 1} \leq - \frac{1}{2} or \frac{3 X - 5}{X - 1} \geq \frac{1}{2}

\frac{3 X - 5}{X - 1} \leq - \frac{1}{2} or \frac{3 X - 5}{X - 1} \geq \frac{1}{2}

1 < X \leq \frac{11}{7} or (X < 1 or X \geq \frac{9}{5})

Merge Overlapping Intervals

X < 1 or 1 < X \leq \frac{11}{7} or X \geq \frac{9}{5}

- 4 (3 t - 9) \geq 8 (- 8 - t)

\frac{b}{15.6} = 11.6

y^{2} + 14 y + 33 = 0

x^{3} + 9 x

\frac{9 !}{2 ! ( 9 - 2 ) !}

What is |((3X-5))/(X-1)|>= 1/2 ?
The solution to |((3X-5))/(X-1)|>= 1/2 is X<1\lor 1<X<= 11/7 \lor X>= 9/5