What is the answer to 5|x-4|-7=-2 ?

The answer to 5|x-4|-7=-2 is x=3\lor x=5

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5|x-4|-7=-2

5 ∣ x - 4 ∣ - 7 = - 2

x = 3 or x = 5

Solution steps

5 ∣ x - 4 ∣ - 7 = - 2

Move

7

to the right side

5 ∣ x - 4 ∣ = 5

Divide both sides by

5

∣ x - 4 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 4 = - 1 or x - 4 = 1

x - 4 = - 1 or x - 4 = 1

x = 3 or x = 5

∣ b + 7 ∣ + 3 = 4

2 x^{2} + 3 x - 20 = 0

∣ v ∣ = - 7

∣ v ∣ = - 5

∣ x - 16 ∣ + 2 = 1