What is 10x+12<12x+30<3x+6 ?

The solution to 10x+12<12x+30<3x+6 is -9<x<-8/3

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10x+12<12x+30<3x+6

10 x + 12 < 12 x + 30 < 3 x + 6

- 9 < x < - \frac{8}{3}

Interval Notation

(- 9, - \frac{8}{3})

Decimal Notation

- 9 < x < - 2.66666 \dots

Solution steps

10 x + 12 < 12 x + 30 < 3 x + 6

a < u < b

then

a < u and u < b

10 x + 12 < 12 x + 30 and 12 x + 30 < 3 x + 6

10 x + 12 < 12 x + 30 : x > - 9

12 x + 30 < 3 x + 6 : x < - \frac{8}{3}

Combine the intervals

x > - 9 and x < - \frac{8}{3}

Merge Overlapping Intervals

- 9 < x < - \frac{8}{3}

x^{2} + 3 x < 5 x^{2} - 2 x < 4 - x^{2}

- 1 < \frac{( 4 - 5 x )}{3} \leq 7

- 4 < 3 x + 2 \leq 5

9 < 2 - 4 x < 12

1 < 3 x - 5 < 2