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

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

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x-1<= 3x+2<= 2x+6

x - 1 \leq 3 x + 2 \leq 2 x + 6

- \frac{3}{2} \leq x \leq 4

Interval Notation

[- \frac{3}{2}, 4]

Decimal Notation

- 1.5 \leq x \leq 4

Solution steps

x - 1 \leq 3 x + 2 \leq 2 x + 6

a \leq u \leq b

then

a \leq u and u \leq b

x - 1 \leq 3 x + 2 and 3 x + 2 \leq 2 x + 6

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

3 x + 2 \leq 2 x + 6 : x \leq 4

Combine the intervals

x \geq - \frac{3}{2} and x \leq 4

Merge Overlapping Intervals

- \frac{3}{2} \leq x \leq 4

4 x = 8

\frac{3 x - 4}{6} + \frac{2 - x}{3} = \frac{1}{2}

\frac{w ^{2} - w - 6}{w - 6} \geq 0

x^{2} + 8 x + 12 > 0

x^{3} - 6 x^{2} - x + 6