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

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

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|x+1|+|x-1|=|2x|

∣ x + 1 ∣ + ∣ x - 1 ∣ = ∣ 2 x ∣

x \leq - 1 or x \geq 1

Solution steps

∣ x + 1 ∣ + ∣ x - 1 ∣ = ∣ 2 x ∣

Find positive and negative intervals

x < - 1, - 1 \leq x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

x < - 1 or x = - 1 or No Solution or x \geq 1

Merge Overlapping Intervals

x \leq - 1 or x \geq 1

∣ 2 x + 5 ∣ + ∣ 2 x - 6 ∣ = 8

(- x^{2} + x - 1)^{3} + x^{2} - x + 1 = 0

∣ x - 1 ∣ ∣ x + 5 ∣ = 7

x^{2} + 6 x + 6 = x^{2} + 4 x + 9 + ∣ 2 x - 3 ∣

x^{2} + 3 x + 2 + x + 1 = 0

What is the answer to |x+1|+|x-1|=|2x| ?
The answer to |x+1|+|x-1|=|2x| is x<=-1\lor x>= 1
Solve for x: |x+1|+|x-1|=|2x|
The solution is x<=-1\lor x>= 1