|2x+1|>x

Solution

∣ 2 x + 1 ∣ > x

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

∣ 2 x + 1 ∣ > x

Find positive and negative intervals

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

Solve the inequality for each interval

x < - \frac{1}{2} or x \geq - \frac{1}{2}

Merge Overlapping Intervals

True for all x

∣ x - 1 ∣ < 0

∣ 3 x - 2 ∣ \leq x + 1

∣ x - 2 ∣ + ∣ x - 1 ∣ > 1

∣ 2 + 3 x ∣ > 0

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