What is the answer to 3|2x+4|+5=5 ?

The answer to 3|2x+4|+5=5 is x=-2

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3|2x+4|+5=5

3 ∣ 2 x + 4 ∣ + 5 = 5

x = - 2

Solution steps

3 ∣ 2 x + 4 ∣ + 5 = 5

Subtract

5

from both sides

3 ∣ 2 x + 4 ∣ + 5 - 5 = 5 - 5

Simplify

3 ∣ 2 x + 4 ∣ = 0

Divide both sides by

3

∣ 2 x + 4 ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

2 x + 4 = 0

2 x + 4 = 0 : x = - 2

x = - 2

∣ 2 x - 4 ∣ - ∣ 3 - x ∣ - 5 = 0

∣ 2 x + 6 ∣ = 8

2 ∣ x - 4 ∣ + 6 = 8

3 \cdot ∣ x ∣ = x^{2} + x - 2

9 + 6 ∣ 7 x + 2 ∣ = - 21