What is | 3/4 x-3|+1<= 15 ?

The solution to | 3/4 x-3|+1<= 15 is -44/3 <= x<= 68/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

| 3/4 x-3|+1<= 15

\frac{3}{4} x - 3 + 1 \leq 15

- \frac{44}{3} \leq x \leq \frac{68}{3}

Interval Notation

[- \frac{44}{3}, \frac{68}{3}]

Decimal Notation

- 14.66666 \dots \leq x \leq 22.66666 \dots

Solution steps

\frac{3}{4} x - 3 + 1 \leq 15

Move

1

to the right side

\frac{3}{4} x - 3 \leq 14

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 14 \leq \frac{3}{4} x - 3 \leq 14

\frac{3}{4} x - 3 \geq - 14 and \frac{3}{4} x - 3 \leq 14

x \geq - \frac{44}{3} and x \leq \frac{68}{3}

Merge Overlapping Intervals

- \frac{44}{3} \leq x \leq \frac{68}{3}

v^{2} - 8 v + 16 = 0

(a - 3)^{2} = 6

\frac{3}{4} x^{2} + 1 = 31

9 a^{2} - 15 a + 4

2 r + (t + r)

What is | 3/4 x-3|+1<= 15 ?
The solution to | 3/4 x-3|+1<= 15 is -44/3 <= x<= 68/3