What is (-3)/5+7 1/2 <= (-7x-11)/2+3<8 ?

The solution to (-3)/5+7 1/2 <= (-7x-11)/2+3<8 is -3<x<=-2 24/35

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(-3)/5+7 1/2 <= (-7x-11)/2+3<8

\frac{- 3}{5} + 7 \frac{1}{2} \leq \frac{- 7 x - 11}{2} + 3 < 8

- 3 < x \leq - 2 \frac{24}{35}

Interval Notation

Decimal

- 3 < x \leq - 2.68571 \dots

Solution steps

\frac{- 3}{5} + 7 \frac{1}{2} \leq \frac{- 7 x - 11}{2} + 3 < 8

Convert mixed numbers to improper fractions:

7 \frac{1}{2} = \frac{15}{2}

\frac{- 3}{5} + \frac{15}{2} \leq \frac{- 7 x - 11}{2} + 3 < 8

a \leq u < b

then

a \leq u and u < b

\frac{- 3}{5} + \frac{15}{2} \leq \frac{- 7 x - 11}{2} + 3 and \frac{- 7 x - 11}{2} + 3 < 8

\frac{- 3}{5} + \frac{15}{2} \leq \frac{- 7 x - 11}{2} + 3 : x \leq - \frac{94}{35}

\frac{- 7 x - 11}{2} + 3 < 8 : x > - 3

Combine the intervals

x \leq - \frac{94}{35} and x > - 3

Merge Overlapping Intervals

- 3 < x \leq - \frac{94}{35}

Convert improper fractions to mixed numbers:

\frac{94}{35} = 2 \frac{24}{35}

- 3 < x \leq - 2 \frac{24}{35}

\frac{1}{2} + \frac{3}{5}

3 \frac{64}{1000}

- 1.8 \leq x \leq - 0.03

3 (4 - 2 y) + 6 y = 12

\frac{5}{8} - \frac{1}{16}

What is (-3)/5+7 1/2 <= (-7x-11)/2+3<8 ?
The solution to (-3)/5+7 1/2 <= (-7x-11)/2+3<8 is -3<x<=-2 24/35