|x(x+1)|>1

Solution

∣ x (x + 1) ∣ > 1

x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}

Interval Notation

(- \infty, \frac{- 5 - 1}{2}) \cup (\frac{5 - 1}{2}, \infty)

Decimal Notation

x < - 1.61803 \dots or x > 0.61803 \dots

Solution steps

∣ x (x + 1) ∣ > 1

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

x (x + 1) < - 1 or x (x + 1) > 1

x (x + 1) < - 1 or x (x + 1) > 1

No Solution or (x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2})

Merge Overlapping Intervals

x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}

(y + 3)^{2} + 7 = 87

∣ 8 - (w - 1) ∣ \leq 9

x^{3} - 16 x

4 x^{2} - 99 = 4 x

x^{2} - x + 11 = 0

What is |x(x+1)|>1 ?
The solution to |x(x+1)|>1 is x<(-sqrt(5)-1)/2 \lor x>(sqrt(5)-1)/2