What is -1/4 |3x+7|+16>8 ?

The solution to -1/4 |3x+7|+16>8 is -13<x< 25/3

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-1/4 |3x+7|+16>8

- \frac{1}{4} ∣ 3 x + 7 ∣ + 16 > 8

- 13 < x < \frac{25}{3}

Solution steps

- \frac{1}{4} ∣ 3 x + 7 ∣ + 16 > 8

Move

16

to the right side

- \frac{1}{4} ∣ 3 x + 7 ∣ > - 8

Multiply both sides by

- 1

\frac{1}{4} ∣ 3 x + 7 ∣ < 8

Multiply both sides by

4

∣ 3 x + 7 ∣ < 32

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 32 < 3 x + 7 < 32

3 x + 7 > - 32 and 3 x + 7 < 32

x > - 13 and x < \frac{25}{3}

Merge Overlapping Intervals

- 13 < x < \frac{25}{3}

- 2 + 23 i

1 \leq x \leq 3

x + 5 x + 8 = 26 - 3 x

\frac{1}{27} y^{9} - \frac{27}{1000} x^{12}

3 x + 5 \geq - 1