What is the answer to |x|+3=15-|x| ?

The answer to |x|+3=15-|x| is x=-6\lor x=6

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|x|+3=15-|x|

∣ x ∣ + 3 = 15 - ∣ x ∣

x = - 6 or x = 6

Solution steps

∣ x ∣ + 3 = 15 - ∣ x ∣

Move

3

to the right side

∣ x ∣ = - ∣ x ∣ + 12

Move

∣ x ∣

to the left side

2 ∣ x ∣ = 12

Divide both sides by

2

∣ x ∣ = 6

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x = - 6 or x = 6

∣ A ∣^{2} = - \frac{1}{3}

5 ∣ x ∣ = 35

∣ 15 x - 5 ∣ = ∣ 35 - 5 x ∣

∣ x - 2 ∣ = 2 - x

∣ 5 - x ∣ = 5