What is (-20)/7 <3z+6<(-11)/5 ?

The solution to (-20)/7 <3z+6<(-11)/5 is -62/21 <z<-41/15

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(-20)/7 <3z+6<(-11)/5

\frac{- 20}{7} < 3 z + 6 < \frac{- 11}{5}

- \frac{62}{21} < z < - \frac{41}{15}

Interval Notation

(- \frac{62}{21}, - \frac{41}{15})

Decimal Notation

- 2.95238 \dots < z < - 2.73333 \dots

Solution steps

\frac{- 20}{7} < 3 z + 6 < \frac{- 11}{5}

a < u < b

then

a < u and u < b

\frac{- 20}{7} < 3 z + 6 and 3 z + 6 < \frac{- 11}{5}

\frac{- 20}{7} < 3 z + 6 : z > - \frac{62}{21}

3 z + 6 < \frac{- 11}{5} : z < - \frac{41}{15}

Combine the intervals

z > - \frac{62}{21} and z < - \frac{41}{15}

Merge Overlapping Intervals

- \frac{62}{21} < z < - \frac{41}{15}

- 1 \leq \frac{( 2 x + 3 )}{5} \leq 3

x - 3 < x - 2 < x - 1

- 2 < 6 - 4 x < 8

- 5 < 2 x + 1 < 7

1 < \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

What is (-20)/7 <3z+6<(-11)/5 ?
The solution to (-20)/7 <3z+6<(-11)/5 is -62/21 <z<-41/15