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

The answer to 2|x-4|=5 is x= 3/2 \lor x= 13/2

Solve for x: 2|x-4|=5

The solution is x= 3/2 \lor x= 13/2

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2 ∣ x - 4 ∣ = 5

x = \frac{3}{2} or x = \frac{13}{2}

Solution steps

2 ∣ x - 4 ∣ = 5

Divide both sides by

2

∣ x - 4 ∣ = \frac{5}{2}

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 4 = - \frac{5}{2} or x - 4 = \frac{5}{2}

x - 4 = - \frac{5}{2} or x - 4 = \frac{5}{2}

x = \frac{3}{2} or x = \frac{13}{2}

2 ∣ x - 4 ∣ = 6

∣ 8 + 5 x ∣ = 14 - x

3 x - 5 + 5 = 38

∣ 9 x - 5 ∣ = 11

∣ 10 + 5 x ∣ = 15