What is -1/2 <(4-3x)/5 < 1/4 ?

The solution to -1/2 <(4-3x)/5 < 1/4 is 11/12 <x< 13/6

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-1/2 <(4-3x)/5 < 1/4

- \frac{1}{2} < \frac{4 - 3 x}{5} < \frac{1}{4}

\frac{11}{12} < x < \frac{13}{6}

Interval Notation

(\frac{11}{12}, \frac{13}{6})

Decimal Notation

0.91666 \dots < x < 2.16666 \dots

Solution steps

- \frac{1}{2} < \frac{4 - 3 x}{5} < \frac{1}{4}

a < u < b

then

a < u and u < b

- \frac{1}{2} < \frac{4 - 3 x}{5} and \frac{4 - 3 x}{5} < \frac{1}{4}

- \frac{1}{2} < \frac{4 - 3 x}{5} : x < \frac{13}{6}

\frac{4 - 3 x}{5} < \frac{1}{4} : x > \frac{11}{12}

Combine the intervals

x < \frac{13}{6} and x > \frac{11}{12}

Merge Overlapping Intervals

\frac{11}{12} < x < \frac{13}{6}

3 x^{2} - x - 7 = 0

x^{2} + 9 x + 8 = 0

x^{2} - 4 x = - 8

- 3 x + 22 < 16

4 t^{2} - 12 t + 9 - w^{2}

What is -1/2 <(4-3x)/5 < 1/4 ?
The solution to -1/2 <(4-3x)/5 < 1/4 is 11/12 <x< 13/6