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

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

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

x > \frac{1}{4}

Interval Notation

(\frac{1}{4}, \infty)

Decimal Notation

x > 0.25

Solution steps

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

a < u < b

then

a < u and u < b

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

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

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

Combine the intervals

x > \frac{1}{4} and x > - \frac{1}{2}

Merge Overlapping Intervals

x > \frac{1}{4}

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

- 5 < 3 x + 4 < 13

\frac{- 101}{3} < 5 \frac{y}{3} + 3 \leq \frac{51}{3}

1 < ∣ z ∣ < 2

25 < x^{2} < 36

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