What is |2x-3|-|x|<= 3 ?

The solution to |2x-3|-|x|<= 3 is 0<= x<= 6

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|2x-3|-|x|<= 3

∣ 2 x - 3 ∣ - ∣ x ∣ \leq 3

0 \leq x \leq 6

Interval Notation

[0, 6]

Solution steps

∣ 2 x - 3 ∣ - ∣ x ∣ \leq 3

Find positive and negative intervals

x < 0, 0 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

No Solution or 0 \leq x < \frac{3}{2} or \frac{3}{2} \leq x \leq 6

Merge Overlapping Intervals

0 \leq x \leq 6

x^{2} - 5 x > x^{2} - ∣ 5 x ∣

∣ 2 x - 3 ∣ < ∣ x + 2 ∣

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

∣ 2 x - 1 ∣ + ∣ x ∣ \leq 10

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