What is 9-2|4x+1|>3 ?

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

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9-2|4x+1|>3

9 - 2 ∣ 4 x + 1 ∣ > 3

- 1 < x < \frac{1}{2}

Solution steps

9 - 2 ∣ 4 x + 1 ∣ > 3

Move

9

to the right side

- 2 ∣ 4 x + 1 ∣ > - 6

Multiply both sides by

- 1

2 ∣ 4 x + 1 ∣ < 6

Divide both sides by

2

∣ 4 x + 1 ∣ < 3

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 3 < 4 x + 1 < 3

4 x + 1 > - 3 and 4 x + 1 < 3

x > - 1 and x < \frac{1}{2}

Merge Overlapping Intervals

- 1 < x < \frac{1}{2}

x + ∣ 3 - 2 x ∣ > ∣ x + 1 ∣ - 1

∣ x - 1 ∣^{x^{4} - 4 x^{3} + 3 x^{2}} < 1

∣ 15 - x ∣ > 25

∣ 2 x - 1 ∣ < ∣ x + 1 ∣

7 x^{2} - 7 x + 12 < ∣ x - 4 ∣