What is (2x-5)/2 <x+3/2 <= (3x+11)/2 ?

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(2x-5)/2 <x+3/2 <= (3x+11)/2

\frac{2 x - 5}{2} < x + \frac{3}{2} \leq \frac{3 x + 11}{2}

x \geq - 8

Interval Notation

[- 8, \infty)

Solution steps

\frac{2 x - 5}{2} < x + \frac{3}{2} \leq \frac{3 x + 11}{2}

a < u \leq b

then

a < u and u \leq b

\frac{2 x - 5}{2} < x + \frac{3}{2} and x + \frac{3}{2} \leq \frac{3 x + 11}{2}

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

True for all

x

x + \frac{3}{2} \leq \frac{3 x + 11}{2} : x \geq - 8

Combine the intervals

True for all x and x \geq - 8

Merge Overlapping Intervals

x \geq - 8

(x - 1) (x + 2) < (x + 1) (x - 1) \leq (x + 3) (x - 1)

1 < x < 7

1 < x < 2

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

x + 3 < 4 x < 6

What is (2x-5)/2 <x+3/2 <= (3x+11)/2 ?
The solution to (2x-5)/2 <x+3/2 <= (3x+11)/2 is x>=-8