What is | 3/4 x-5|+1<= 16 ?

The solution to | 3/4 x-5|+1<= 16 is -40/3 <= x<= 80/3

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| 3/4 x-5|+1<= 16

\frac{3}{4} x - 5 + 1 \leq 16

- \frac{40}{3} \leq x \leq \frac{80}{3}

Interval Notation

[- \frac{40}{3}, \frac{80}{3}]

Decimal Notation

- 13.33333 \dots \leq x \leq 26.66666 \dots

Solution steps

\frac{3}{4} x - 5 + 1 \leq 16

Move

1

to the right side

\frac{3}{4} x - 5 \leq 15

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 15 \leq \frac{3}{4} x - 5 \leq 15

\frac{3}{4} x - 5 \geq - 15 and \frac{3}{4} x - 5 \leq 15

x \geq - \frac{40}{3} and x \leq \frac{80}{3}

Merge Overlapping Intervals

- \frac{40}{3} \leq x \leq \frac{80}{3}

(x + 3)^{2} = 3

\frac{9}{8} \cdot \frac{2}{3}

- \frac{1}{4} + \frac{1}{8}

\frac{1}{2} c + 3 < \frac{3}{4}

x = \frac{350}{100} \cdot 1

What is | 3/4 x-5|+1<= 16 ?
The solution to | 3/4 x-5|+1<= 16 is -40/3 <= x<= 80/3