What is x|x+1|+|x|>3 ?

The solution to x|x+1|+|x|>3 is x>1

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x|x+1|+|x|>3

x ∣ x + 1 ∣ + ∣ x ∣ > 3

x > 1

Solution steps

x ∣ x + 1 ∣ + ∣ x ∣ > 3

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x > 1

Merge Overlapping Intervals

x > 1

∣ 3 - 5 x ∣ \leq 10

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

x^{2} - 3 x + 2 + 2 x - 1 < 0

∣ 3 x + 3 ∣ \leq 2 x + 2

\frac{( 2 x - 1 )}{( x - 1 )} > 2