What is the answer to 8=|2+4x| ?

The answer to 8=|2+4x| is x=-5/2 \lor x= 3/2

Solve for x: 8=|2+4x|

The solution is x=-5/2 \lor x= 3/2

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8 = ∣ 2 + 4 x ∣

x = - \frac{5}{2} or x = \frac{3}{2}

Solution steps

8 = ∣ 2 + 4 x ∣

Switch sides

∣ 2 + 4 x ∣ = 8

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

2 + 4 x = - 8 or 2 + 4 x = 8

2 + 4 x = - 8 or 2 + 4 x = 8

x = - \frac{5}{2} or x = \frac{3}{2}

2 ∣ x - 3 ∣ + 4 = 8

1 + x^{3} - 3 x = 0

∣ x ∣ - 18 = - 10

∣ - 8 x ∣ = 64

- 3 = - ∣ k ∣