What is |(2x-1)/9 |<= 5/9 ?

The solution to |(2x-1)/9 |<= 5/9 is -2<= x<= 3

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|(2x-1)/9 |<= 5/9

\frac{2 x - 1}{9} \leq \frac{5}{9}

- 2 \leq x \leq 3

Interval Notation

[- 2, 3]

Solution steps

\frac{2 x - 1}{9} \leq \frac{5}{9}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{5}{9} \leq \frac{2 x - 1}{9} \leq \frac{5}{9}

\frac{2 x - 1}{9} \geq - \frac{5}{9} and \frac{2 x - 1}{9} \leq \frac{5}{9}

x \geq - 2 and x \leq 3

Merge Overlapping Intervals

- 2 \leq x \leq 3

3 r^{2} - 10 r + 8

\frac{1}{6} \leq \frac{2 x - 13}{12} \leq \frac{2}{3}

5 x^{2} - 13 x - 6

∣ 5 x + 4 \geq 8 x - 1

y^{2} - \frac{2}{3} y + \frac{1}{9} = 0