What is -5|3-3x|+4>-56 ?

The solution to -5|3-3x|+4>-56 is -3<x<5

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-5|3-3x|+4>-56

- 5 ∣ 3 - 3 x ∣ + 4 > - 56

- 3 < x < 5

Interval Notation

(- 3, 5)

Solution steps

- 5 ∣ 3 - 3 x ∣ + 4 > - 56

Move

4

to the right side

- 5 ∣ 3 - 3 x ∣ > - 60

Multiply both sides by

- 1

5 ∣ 3 - 3 x ∣ < 60

Divide both sides by

5

∣ 3 - 3 x ∣ < 12

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 12 < 3 - 3 x < 12

3 - 3 x > - 12 and 3 - 3 x < 12

x < 5 and x > - 3

Merge Overlapping Intervals

- 3 < x < 5

\frac{12}{7} + \frac{4}{7} + \frac{20}{7}

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

x - \frac{5}{3} = \frac{2 x}{4} + 1

2 x^{2} - 20 x + 48

x^{4} - 3 x^{3} + 8 x - 24