What is -5|6-x|-5>-45 ?

The solution to -5|6-x|-5>-45 is -2<x<14

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-5|6-x|-5>-45

- 5 ∣ 6 - x ∣ - 5 > - 45

- 2 < x < 14

Interval Notation

(- 2, 14)

Solution steps

- 5 ∣ 6 - x ∣ - 5 > - 45

Move

5

to the right side

- 5 ∣ 6 - x ∣ > - 40

Multiply both sides by

- 1

5 ∣ 6 - x ∣ < 40

Divide both sides by

5

∣ 6 - x ∣ < 8

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 8 < 6 - x < 8

6 - x > - 8 and 6 - x < 8

x < 14 and x > - 2

Merge Overlapping Intervals

- 2 < x < 14

\frac{2 ( \frac{5}{12} )}{1 - ( \frac{5}{12} ) ^{2}}

\frac{5 x + 2}{x - 1} = 3

y^{2} - 3 y + 1 = 0

x^{3} - x

4 \cdot 41