What is 4|x-2|-2-x<4x+1 ?

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4|x-2|-2-x<4x+1

4 ∣ x - 2 ∣ - 2 - x < 4 x + 1

x > \frac{5}{9}

Solution steps

4 ∣ x - 2 ∣ - 2 - x < 4 x + 1

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

\frac{5}{9} < x < 2 or x \geq 2

Merge Overlapping Intervals

x > \frac{5}{9}

∣ x - 6 ∣ \geq 4

2 x - 7 x + 12 < ∣ x - 4 ∣

3 ∣ x - 1 ∣ + 2 ∣ x - 2 ∣ + ∣ x - 3 ∣ > 4

\frac{( 3 x - 4 )}{2} < \frac{5}{12}

\frac{( x + 1 )}{( x - 3 )} < \frac{1}{3}