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

The solution to 1/3 <= (x+1)/5 < 5/4 is 2/3 <= x< 21/4

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1/3 <= (x+1)/5 < 5/4

\frac{1}{3} \leq \frac{x + 1}{5} < \frac{5}{4}

\frac{2}{3} \leq x < \frac{21}{4}

Interval Notation

[\frac{2}{3}, \frac{21}{4})

Decimal Notation

0.66666 \dots \leq x < 5.25

Solution steps

\frac{1}{3} \leq \frac{x + 1}{5} < \frac{5}{4}

a \leq u < b

then

a \leq u and u < b

\frac{1}{3} \leq \frac{x + 1}{5} and \frac{x + 1}{5} < \frac{5}{4}

\frac{1}{3} \leq \frac{x + 1}{5} : x \geq \frac{2}{3}

\frac{x + 1}{5} < \frac{5}{4} : x < \frac{21}{4}

Combine the intervals

x \geq \frac{2}{3} and x < \frac{21}{4}

Merge Overlapping Intervals

\frac{2}{3} \leq x < \frac{21}{4}

6 (4 x - 10) = 84

3 x^{2} + 4 x = 1

- 10 \leq \frac{x}{- 2}

∣ 5 y + 3 ∣ = 7

2 (x - 1) - x = 16

What is 1/3 <= (x+1)/5 < 5/4 ?
The solution to 1/3 <= (x+1)/5 < 5/4 is 2/3 <= x< 21/4