What is -3|10+2x|+5>-7 ?

The solution to -3|10+2x|+5>-7 is -7<x<-3

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-3|10+2x|+5>-7

- 3 ∣ 10 + 2 x ∣ + 5 > - 7

- 7 < x < - 3

Interval Notation

(- 7, - 3)

Solution steps

- 3 ∣ 10 + 2 x ∣ + 5 > - 7

Move

5

to the right side

- 3 ∣ 10 + 2 x ∣ > - 12

Multiply both sides by

- 1

3 ∣ 10 + 2 x ∣ < 12

Divide both sides by

3

∣ 10 + 2 x ∣ < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < 10 + 2 x < 4

10 + 2 x > - 4 and 10 + 2 x < 4

x > - 7 and x < - 3

Merge Overlapping Intervals

- 7 < x < - 3

\frac{1}{4} + 2 x = \frac{7}{2}

(- 0.008)^{\frac{2}{3}}

1000 - i 900

\frac{4 ^{2}}{2 ^{2}}

5 x^{2} + 11 x + 6 = 0