What is |(2x-5)/3 |<= 1/4 ?

The solution to |(2x-5)/3 |<= 1/4 is 17/8 <= x<= 23/8

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|(2x-5)/3 |<= 1/4

\frac{2 x - 5}{3} \leq \frac{1}{4}

\frac{17}{8} \leq x \leq \frac{23}{8}

Interval Notation

[\frac{17}{8}, \frac{23}{8}]

Decimal Notation

2.125 \leq x \leq 2.875

Solution steps

\frac{2 x - 5}{3} \leq \frac{1}{4}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{4} \leq \frac{2 x - 5}{3} \leq \frac{1}{4}

\frac{2 x - 5}{3} \geq - \frac{1}{4} and \frac{2 x - 5}{3} \leq \frac{1}{4}

x \geq \frac{17}{8} and x \leq \frac{23}{8}

Merge Overlapping Intervals

\frac{17}{8} \leq x \leq \frac{23}{8}

3 x^{2} - 17 x = 6

\frac{π}{2} + \frac{π}{2}

2 x^{2} + 16 = - 20

x^{2} - 8 x = 242

(- 5 x y^{4})^{2}

What is |(2x-5)/3 |<= 1/4 ?
The solution to |(2x-5)/3 |<= 1/4 is 17/8 <= x<= 23/8