What is |x+5|>|x-5| ?

The solution to |x+5|>|x-5| is x>0

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|x+5|>|x-5|

∣ x + 5 ∣ > ∣ x - 5 ∣

x > 0

Solution steps

∣ x + 5 ∣ > ∣ x - 5 ∣

Find positive and negative intervals

x < - 5, - 5 \leq x < 5, x \geq 5

Solve the inequality for each interval

No Solution or 0 < x < 5 or x \geq 5

Merge Overlapping Intervals

x > 0

x^{2} - 1 \leq ∣ x + 3 ∣

x^{2} - 3 x - 4 < x + 1

∣ - 2 x + 2 ∣ - 1 > 5

x^{2} - 5 x \geq 6

∣ x + 2 ∣ > 3 x