What is |((x-7))/((4x-15))|>8 ?

The solution to |((x-7))/((4x-15))|>8 is 113/31 <x< 15/4 \lor 15/4 <x< 127/33

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|((x-7))/((4x-15))|>8

\frac{( x - 7 )}{( 4 x - 15 )} > 8

\frac{113}{31} < x < \frac{15}{4} or \frac{15}{4} < x < \frac{127}{33}

Interval Notation

(\frac{113}{31}, \frac{15}{4}) \cup (\frac{15}{4}, \frac{127}{33})

Decimal Notation

3.64516 \dots < x < 3.75 or 3.75 < x < 3.84848 \dots

Solution steps

\frac{x - 7}{4 x - 15} > 8

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

\frac{x - 7}{4 x - 15} < - 8 or \frac{x - 7}{4 x - 15} > 8

\frac{x - 7}{4 x - 15} < - 8 or \frac{x - 7}{4 x - 15} > 8

\frac{113}{31} < x < \frac{15}{4} or \frac{15}{4} < x < \frac{127}{33}

- 16 = \frac{8 x}{5}

3 n^{2} + 8 n + 16 = 2 n^{2}

2 \geq \frac{n}{4} - 2

4 x + 3 < 15

m^{2} + 2 m + 5 = 0

What is |((x-7))/((4x-15))|>8 ?
The solution to |((x-7))/((4x-15))|>8 is 113/31 <x< 15/4 \lor 15/4 <x< 127/33