What is 1-|4q+2|>-9 ?

The solution to 1-|4q+2|>-9 is -3<q<2

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1-|4q+2|>-9

1 - ∣ 4 q + 2 ∣ > - 9

- 3 < q < 2

Interval Notation

(- 3, 2)

Solution steps

1 - ∣ 4 q + 2 ∣ > - 9

Move

1

to the right side

- ∣ 4 q + 2 ∣ > - 10

Multiply both sides by

- 1

∣ 4 q + 2 ∣ < 10

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 10 < 4 q + 2 < 10

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

q > - 3 and q < 2

Merge Overlapping Intervals

- 3 < q < 2

4 x = 2 x + 4

2 - \frac{x}{3} = 2

w^{2} = - 2 w - 16

x^{2} - 6 x = 13

\frac{j - 91}{- 4} = - 2