What is 1/7 <= (1-7t)/8 < 7/8 ?

The solution to 1/7 <= (1-7t)/8 < 7/8 is -6/7 <t<=-1/49

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1/7 <= (1-7t)/8 < 7/8

\frac{1}{7} \leq \frac{1 - 7 t}{8} < \frac{7}{8}

- \frac{6}{7} < t \leq - \frac{1}{49}

Interval Notation

(- \frac{6}{7}, - \frac{1}{49}]

Decimal Notation

- 0.85714 \dots < t \leq - 0.02040 \dots

Solution steps

\frac{1}{7} \leq \frac{1 - 7 t}{8} < \frac{7}{8}

a \leq u < b

then

a \leq u and u < b

\frac{1}{7} \leq \frac{1 - 7 t}{8} and \frac{1 - 7 t}{8} < \frac{7}{8}

\frac{1}{7} \leq \frac{1 - 7 t}{8} : t \leq - \frac{1}{49}

\frac{1 - 7 t}{8} < \frac{7}{8} : t > - \frac{6}{7}

Combine the intervals

t \leq - \frac{1}{49} and t > - \frac{6}{7}

Merge Overlapping Intervals

- \frac{6}{7} < t \leq - \frac{1}{49}

(x + 1)^{2} = 81

\frac{1}{7} x - 5 = 8

n^{2} - 24 n - 25

- \frac{8}{4}

3 x + 3 (x + y)

What is 1/7 <= (1-7t)/8 < 7/8 ?
The solution to 1/7 <= (1-7t)/8 < 7/8 is -6/7 <t<=-1/49