What is 1/4 <= (x+1)/5 < 5/2 ?

The solution to 1/4 <= (x+1)/5 < 5/2 is 1/4 <= x< 23/2

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1/4 <= (x+1)/5 < 5/2

\frac{1}{4} \leq \frac{x + 1}{5} < \frac{5}{2}

\frac{1}{4} \leq x < \frac{23}{2}

Interval Notation

[\frac{1}{4}, \frac{23}{2})

Decimal Notation

0.25 \leq x < 11.5

Solution steps

\frac{1}{4} \leq \frac{x + 1}{5} < \frac{5}{2}

a \leq u < b

then

a \leq u and u < b

\frac{1}{4} \leq \frac{x + 1}{5} and \frac{x + 1}{5} < \frac{5}{2}

\frac{1}{4} \leq \frac{x + 1}{5} : x \geq \frac{1}{4}

\frac{x + 1}{5} < \frac{5}{2} : x < \frac{23}{2}

Combine the intervals

x \geq \frac{1}{4} and x < \frac{23}{2}

Merge Overlapping Intervals

\frac{1}{4} \leq x < \frac{23}{2}

- \frac{2}{3} + 3

∣ 4 x + 4 ∣ + 9 < 1

8 x + 9 < 4 x - 3

3 x + 9 + 4 x + x = 8 x + 7

3 x - 5 > 4

What is 1/4 <= (x+1)/5 < 5/2 ?
The solution to 1/4 <= (x+1)/5 < 5/2 is 1/4 <= x< 23/2