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

The solution to 1/2 <= ((1-2t))/3 < 2/3 is -1/2 <t<=-1/4

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1/2 <= ((1-2t))/3 < 2/3

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

- \frac{1}{2} < t \leq - \frac{1}{4}

Interval Notation

(- \frac{1}{2}, - \frac{1}{4}]

Decimal Notation

- 0.5 < t \leq - 0.25

Solution steps

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

a \leq u < b

then

a \leq u and u < b

\frac{1}{2} \leq \frac{( 1 - 2 t )}{3} and \frac{( 1 - 2 t )}{3} < \frac{2}{3}

\frac{1}{2} \leq \frac{1 - 2 t}{3} : t \leq - \frac{1}{4}

\frac{1 - 2 t}{3} < \frac{2}{3} : t > - \frac{1}{2}

Combine the intervals

t \leq - \frac{1}{4} and t > - \frac{1}{2}

Merge Overlapping Intervals

- \frac{1}{2} < t \leq - \frac{1}{4}

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