What is |x+1|+|x-1|>2x ?

The solution 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 < 1

Solution steps

∣ x + 1 ∣ + ∣ x - 1 ∣ > 2 x

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 1 or - 1 \leq x < 1 or No Solution

Merge Overlapping Intervals

x < 1

4 x^{2} - 1 + x^{2} - 4 \geq 6

- 3 ∣ 6 - x ∣ < - 15

∣ x - 1 ∣ + ∣ x - 2 ∣ + 2 ∣ x - 3 ∣ < 0

\frac{( x - 1 )}{( x - 2 )} \leq 3

\frac{( 3 - 4 x )}{5} \leq 4