What is (-25)/6 < 1/2-2 x/3 <2 ?

The solution to (-25)/6 < 1/2-2 x/3 <2 is -9/4 <x<7

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(-25)/6 < 1/2-2 x/3 <2

\frac{- 25}{6} < \frac{1}{2} - 2 \frac{x}{3} < 2

- \frac{9}{4} < x < 7

Interval Notation

(- \frac{9}{4}, 7)

Decimal Notation

- 2.25 < x < 7

Solution steps

\frac{- 25}{6} < \frac{1}{2} - 2 \cdot \frac{x}{3} < 2

a < u < b

then

a < u and u < b

\frac{- 25}{6} < \frac{1}{2} - 2 \cdot \frac{x}{3} and \frac{1}{2} - 2 \cdot \frac{x}{3} < 2

\frac{- 25}{6} < \frac{1}{2} - 2 \cdot \frac{x}{3} : x < 7

\frac{1}{2} - 2 \cdot \frac{x}{3} < 2 : x > - \frac{9}{4}

Combine the intervals

x < 7 and x > - \frac{9}{4}

Merge Overlapping Intervals

- \frac{9}{4} < x < 7

\frac{- 1}{2} < \frac{x}{( x ^{2} - x - 1 )} < 2

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

x + 1 < 3 x - 5 < 4 x - 7

- 12 < 4 - 3 \frac{x}{- 5} \leq 2

44 < x < 45

What is (-25)/6 < 1/2-2 x/3 <2 ?
The solution to (-25)/6 < 1/2-2 x/3 <2 is -9/4 <x<7