What is -5|x-3|-5<15 ?

The solution to -5|x-3|-5<15 is True for all x

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-5|x-3|-5<15

- 5 ∣ x - 3 ∣ - 5 < 15

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

- 5 ∣ x - 3 ∣ - 5 < 15

Move

5

to the right side

- 5 ∣ x - 3 ∣ < 20

Multiply both sides by

- 1

5 ∣ x - 3 ∣ > - 20

Divide both sides by

5

∣ x - 3 ∣ > - 4

Absolute values are always greater or equal to 0

True for all x

∣ 4 x - 3 ∣ \leq 4 - 3 x

∣ x - 28 ∣ \leq 2

x^{2} - 2 x - 3 > x^{2} + 7 x - 13

\frac{( 2 x ^{2} - 4 )}{3} \geq 2 x^{2}

∣ x + 1 ∣ < ∣ 2 x - 1 ∣