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

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

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

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

1 < x \leq \frac{13}{3}

Interval Notation

(1, \frac{13}{3}]

Decimal Notation

1 < x \leq 4.33333 \dots

Solution steps

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

a \leq u < b

then

a \leq u and u < b

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

- 2 \leq \frac{5 - 3 x}{4} : x \leq \frac{13}{3}

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

Combine the intervals

x \leq \frac{13}{3} and x > 1

Merge Overlapping Intervals

1 < x \leq \frac{13}{3}

- 7 < 2 x - 3 < 9

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

1 < 2 x < 3

13 < 5 x - 8 < 23

\frac{- 1}{5} \leq \frac{( 2 x )}{5} + 1 < \frac{1}{5}

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