|x-2|<2x

Solution

∣ x - 2 ∣ < 2 x

x > \frac{2}{3}

Interval Notation

(\frac{2}{3}, \infty)

Decimal Notation

x > 0.66666 \dots

Solution steps

∣ x - 2 ∣ < 2 x

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

\frac{2}{3} < x < 2 or x \geq 2

Merge Overlapping Intervals

x > \frac{2}{3}

16 + 7 x - 5 + x = 11 x - 3 - x

(x - 3)^{2} + 10 (x - 3) + 9 = 0

- x^{2} + 4 x = 10

5 x + 1 = 2 x - 5

\frac{3 x}{4} - 7 = - 9