What is the answer to -5=-3|x-3|+4 ?

The answer to -5=-3|x-3|+4 is x=0\lor x=6

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-5=-3|x-3|+4

- 5 = - 3 ∣ x - 3 ∣ + 4

x = 0 or x = 6

Solution steps

- 5 = - 3 ∣ x - 3 ∣ + 4

Switch sides

- 3 ∣ x - 3 ∣ + 4 = - 5

Move

4

to the right side

- 3 ∣ x - 3 ∣ = - 9

Divide both sides by

- 3

∣ x - 3 ∣ = 3

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 3 = - 3 or x - 3 = 3

x - 3 = - 3 or x - 3 = 3

x = 0 or x = 6

4 ∣ x ∣ = - 2

∣ 5 x - 2 ∣ = 11

∣ 5 x - 2 ∣ = 18

11 ∣ x - 9 ∣ = 121

∣ x - 2 ∣ = - x^{2} + 4 x - 2