What is |x+2|+|x-3|<|2x+1| ?

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|x+2|+|x-3|<|2x+1|

∣ x + 2 ∣ + ∣ x - 3 ∣ < ∣ 2 x + 1 ∣

x > 2

Solution steps

∣ x + 2 ∣ + ∣ x - 3 ∣ < ∣ 2 x + 1 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < - \frac{1}{2}, - \frac{1}{2} \leq x < 3, x \geq 3

Solve the inequality for each interval

No Solution or 2 < x < 3 or x \geq 3

Merge Overlapping Intervals

x > 2

x^{2} - 2 x - 3 < 3 x - 3

x^{3} - 1 \leq x^{2} + x + 1

∣ 2 x ∣ + 4 > 0

∣ 2 x - 3 ∣ - ∣ x ∣ \leq 3

x^{2} - 5 x > x^{2} - ∣ 5 x ∣