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

The solution to ((3x-1))/6 <= ((2x+1))/3 <= ((x+2))/2 is -3<= x<= 4

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((3x-1))/6 <= ((2x+1))/3 <= ((x+2))/2

\frac{( 3 x - 1 )}{6} \leq \frac{( 2 x + 1 )}{3} \leq \frac{( x + 2 )}{2}

- 3 \leq x \leq 4

Interval Notation

[- 3, 4]

Solution steps

\frac{( 3 x - 1 )}{6} \leq \frac{( 2 x + 1 )}{3} \leq \frac{( x + 2 )}{2}

a \leq u \leq b

then

a \leq u and u \leq b

\frac{( 3 x - 1 )}{6} \leq \frac{( 2 x + 1 )}{3} and \frac{( 2 x + 1 )}{3} \leq \frac{( x + 2 )}{2}

\frac{3 x - 1}{6} \leq \frac{2 x + 1}{3} : x \geq - 3

\frac{2 x + 1}{3} \leq \frac{x + 2}{2} : x \leq 4

Combine the intervals

x \geq - 3 and x \leq 4

Merge Overlapping Intervals

- 3 \leq x \leq 4

0 < 2 x - \frac{5}{2} < 7

- 3 \leq 4 - \frac{( 7 x )}{x} \leq 18

1 \leq x^{2} \leq 4

9 < x < 11

3 x < 15 < 5 x

What is ((3x-1))/6 <= ((2x+1))/3 <= ((x+2))/2 ?
The solution to ((3x-1))/6 <= ((2x+1))/3 <= ((x+2))/2 is -3<= x<= 4