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

The solution to |(3x-4)/3 |<= 1/5 is 17/15 <= x<= 23/15

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

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

\frac{17}{15} \leq x \leq \frac{23}{15}

Interval Notation

[\frac{17}{15}, \frac{23}{15}]

Decimal Notation

1.13333 \dots \leq x \leq 1.53333 \dots

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

x \geq \frac{17}{15} and x \leq \frac{23}{15}

Merge Overlapping Intervals

\frac{17}{15} \leq x \leq \frac{23}{15}

12 n^{2} + 58 n + 56

4 x = 4 + 2 x

\frac{3 ( x - 4 )}{2} \geq \frac{2 x}{3} - 9

2 d + 7 < - 9

9 c^{2} + 24 c - 20

What is |(3x-4)/3 |<= 1/5 ?
The solution to |(3x-4)/3 |<= 1/5 is 17/15 <= x<= 23/15