What is |(2x-7)/4 |<= 1/5 ?

The solution to |(2x-7)/4 |<= 1/5 is 31/10 <= x<= 39/10

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|(2x-7)/4 |<= 1/5

\frac{2 x - 7}{4} \leq \frac{1}{5}

\frac{31}{10} \leq x \leq \frac{39}{10}

Interval Notation

[\frac{31}{10}, \frac{39}{10}]

Decimal Notation

3.1 \leq x \leq 3.9

Solution steps

\frac{2 x - 7}{4} \leq \frac{1}{5}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{5} \leq \frac{2 x - 7}{4} \leq \frac{1}{5}

\frac{2 x - 7}{4} \geq - \frac{1}{5} and \frac{2 x - 7}{4} \leq \frac{1}{5}

x \geq \frac{31}{10} and x \leq \frac{39}{10}

Merge Overlapping Intervals

\frac{31}{10} \leq x \leq \frac{39}{10}

(\frac{1}{4 ab})^{- 2}

\frac{x + 1}{4} - \frac{1}{6} = \frac{2 - x}{3}

\frac{9 - x}{6} = 5

10 x < 50

\frac{1}{- \frac{1}{4} + 2}

What is |(2x-7)/4 |<= 1/5 ?
The solution to |(2x-7)/4 |<= 1/5 is 31/10 <= x<= 39/10