What is |2x|3-x|-2|<= 4 ?

The solution to |2x|3-x|-2|<= 4 is -1/2 <= x<= 1

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|2x|3-x|-2|<= 4

∣ 2 x ∣ 3 - x ∣ - 2 ∣ \leq 4

- \frac{1}{2} \leq x \leq 1

Solution steps

∣ 2 x ∣ \cdot 3 - x ∣ - 2 ∣ \leq 4

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- \frac{1}{2} \leq x < 0 or 0 \leq x \leq 1

Merge Overlapping Intervals

- \frac{1}{2} \leq x \leq 1

∣ 2 x - 11 ∣ > - 3

\frac{x + 2}{x} < 3

∣ x ∣ + ∣ x - 1 ∣ + ∣ x + 2 ∣ > 4

∣ x - 1 ∣ \geq \frac{( x + 1 )}{2}

x^{2} + x > ∣ x + 2 ∣