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

The solution to ((2x-1))/3 <x+((5-x))/2 <= 3/5+((x+1))/3 is x<=-47/5

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

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

x \leq - \frac{47}{5}

Interval Notation

(- \infty, - \frac{47}{5}]

Decimal Notation

x \leq - 9.4

Solution steps

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

a < u \leq b

then

a < u and u \leq b

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

\frac{2 x - 1}{3} < x + \frac{5 - x}{2} : x < 17

x + \frac{5 - x}{2} \leq \frac{3}{5} + \frac{x + 1}{3} : x \leq - \frac{47}{5}

Combine the intervals

x < 17 and x \leq - \frac{47}{5}

Merge Overlapping Intervals

x \leq - \frac{47}{5}

- 5 < 3 x + 4 < 13

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

1 < ∣ z ∣ < 2

25 < x^{2} < 36

1 < x < 20

What is ((2x-1))/3 <x+((5-x))/2 <= 3/5+((x+1))/3 ?
The solution to ((2x-1))/3 <x+((5-x))/2 <= 3/5+((x+1))/3 is x<=-47/5