What is 11-2|x+4|>8 ?

The solution to 11-2|x+4|>8 is -11/2 <x<-5/2

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11-2|x+4|>8

11 - 2 ∣ x + 4 ∣ > 8

- \frac{11}{2} < x < - \frac{5}{2}

Interval Notation

(- \frac{11}{2}, - \frac{5}{2})

Decimal Notation

- 5.5 < x < - 2.5

Solution steps

11 - 2 ∣ x + 4 ∣ > 8

Move

11

to the right side

- 2 ∣ x + 4 ∣ > - 3

Multiply both sides by

- 1

2 ∣ x + 4 ∣ < 3

Divide both sides by

2

∣ x + 4 ∣ < \frac{3}{2}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{3}{2} < x + 4 < \frac{3}{2}

x + 4 > - \frac{3}{2} and x + 4 < \frac{3}{2}

x > - \frac{11}{2} and x < - \frac{5}{2}

Merge Overlapping Intervals

- \frac{11}{2} < x < - \frac{5}{2}

6 x^{5} - 48 x^{2}

3 (x + 4) > 21

4^{l o g_{2} (n)}

4 (- 8 x + 5) = - 32 x - 26

5 (x - 2) = 2 (x - 7)