What is the answer to 2x-7=|x|+1 ?

The answer to 2x-7=|x|+1 is x=8

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2x-7=|x|+1

2 x - 7 = ∣ x ∣ + 1

x = 8

Solution steps

2 x - 7 = ∣ x ∣ + 1

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

No Solution or x = 8

x = 8

x^{2} - 12 = x

- 5 ∣ 2 - 2 x ∣ = - 50

∣ x ∣ = 33

∣ x - 7 ∣ = - 6

∣ x - 7 ∣ = - 2