|x-2|<4

Solution

∣ x - 2 ∣ < 4

- 2 < x < 6

Interval Notation

(- 2, 6)

Solution steps

∣ x - 2 ∣ < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < x - 2 < 4

x - 2 > - 4 and x - 2 < 4

x > - 2 and x < 6

Merge Overlapping Intervals

- 2 < x < 6

2 x^{2} - 4 x + 5 = 3

30 x - (- x + 6) + (- 5 x + 4) = - (5 x + 6) + (- 8 + 3 x)

\frac{a - \frac{a}{b}}{b - \frac{b}{a}}

2 k^{2} + 3 k - 9