What is | 3/4 x+1/3 |<= 1/12 ?

The solution to | 3/4 x+1/3 |<= 1/12 is -5/9 <= x<=-1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

| 3/4 x+1/3 |<= 1/12

\frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

- \frac{5}{9} \leq x \leq - \frac{1}{3}

Interval Notation

[- \frac{5}{9}, - \frac{1}{3}]

Decimal Notation

- 0.55555 \dots \leq x \leq - 0.33333 \dots

Solution steps

\frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{12} \leq \frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

\frac{3}{4} x + \frac{1}{3} \geq - \frac{1}{12} and \frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

x \geq - \frac{5}{9} and x \leq - \frac{1}{3}

Merge Overlapping Intervals

- \frac{5}{9} \leq x \leq - \frac{1}{3}

x^{2} + 2 x - 5 = 0

- 4 < 8

x^{4} + 12 x^{3} + 31 x^{2} - 12 x - 32

3 x^{2} + 6 x + 2 = 0

(3 - 2)^{2}

What is | 3/4 x+1/3 |<= 1/12 ?
The solution to | 3/4 x+1/3 |<= 1/12 is -5/9 <= x<=-1/3