What is -1/3 <= (2x)/3-3<= 2/7 ?

The solution to -1/3 <= (2x)/3-3<= 2/7 is 4<= x<= 69/14

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-1/3 <= (2x)/3-3<= 2/7

- \frac{1}{3} \leq \frac{2 x}{3} - 3 \leq \frac{2}{7}

4 \leq x \leq \frac{69}{14}

Interval Notation

[4, \frac{69}{14}]

Decimal Notation

4 \leq x \leq 4.92857 \dots

Solution steps

- \frac{1}{3} \leq \frac{2 x}{3} - 3 \leq \frac{2}{7}

a \leq u \leq b

then

a \leq u and u \leq b

- \frac{1}{3} \leq \frac{2 x}{3} - 3 and \frac{2 x}{3} - 3 \leq \frac{2}{7}

- \frac{1}{3} \leq \frac{2 x}{3} - 3 : x \geq 4

\frac{2 x}{3} - 3 \leq \frac{2}{7} : x \leq \frac{69}{14}

Combine the intervals

x \geq 4 and x \leq \frac{69}{14}

Merge Overlapping Intervals

4 \leq x \leq \frac{69}{14}

2 x^{2} - 13 x = - 15

14 x^{3} - 7 x^{2} - 35 x

\frac{x}{x - 2} < 2

24 x^{2} - 46 x = 18

3 x^{2} + 4 x - 9 = 0

What is -1/3 <= (2x)/3-3<= 2/7 ?
The solution to -1/3 <= (2x)/3-3<= 2/7 is 4<= x<= 69/14