What is -21<= (2x)/3-1/4 <7 ?

The solution to -21<= (2x)/3-1/4 <7 is -249/8 <= x< 87/8

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-21<= (2x)/3-1/4 <7

- 21 \leq \frac{2 x}{3} - \frac{1}{4} < 7

- \frac{249}{8} \leq x < \frac{87}{8}

Interval Notation

[- \frac{249}{8}, \frac{87}{8})

Decimal Notation

- 31.125 \leq x < 10.875

Solution steps

- 21 \leq \frac{2 x}{3} - \frac{1}{4} < 7

a \leq u < b

then

a \leq u and u < b

- 21 \leq \frac{2 x}{3} - \frac{1}{4} and \frac{2 x}{3} - \frac{1}{4} < 7

- 21 \leq \frac{2 x}{3} - \frac{1}{4} : x \geq - \frac{249}{8}

\frac{2 x}{3} - \frac{1}{4} < 7 : x < \frac{87}{8}

Combine the intervals

x \geq - \frac{249}{8} and x < \frac{87}{8}

Merge Overlapping Intervals

- \frac{249}{8} \leq x < \frac{87}{8}

- 12 x < 60

x^{2} + 2 x = - 5

x^{- 2} - 3^{- 2}

3 x + 9 - 2 < 7

3 (k - 2) - 4 k (k - 2)

What is -21<= (2x)/3-1/4 <7 ?
The solution to -21<= (2x)/3-1/4 <7 is -249/8 <= x< 87/8