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

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

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|x-1|+x=1

∣ x - 1 ∣ + x = 1

x \leq 1

Solution steps

∣ x - 1 ∣ + x = 1

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

x < 1 or x = 1

Merge Overlapping Intervals

x \leq 1

∣ x - a ∣ = ∣ x - 4 ∣

∣ 3 x - 2 ∣ = - 4

∣ x - 1 ∣ + ∣ 2 x - 4 ∣ = 5

6 x^{2} - 5 x - 1 = 5 x - 6 x^{2} + 1

∣ x - 1 ∣ + ∣ x - 5 ∣ = 6