What is |(x+1)(x+3)|< x/2+2 ?

The solution to |(x+1)(x+3)|< x/2+2 is (-sqrt(33)-7)/4 <x<-5/2 \lor-2<x<(sqrt(33)-7)/4

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|(x+1)(x+3)|< x/2+2

∣ (x + 1) (x + 3) ∣ < \frac{x}{2} + 2

\frac{- 33 - 7}{4} < x < - \frac{5}{2} or - 2 < x < \frac{33 - 7}{4}

Interval Notation

(\frac{- 33 - 7}{4}, - \frac{5}{2}) \cup (- 2, \frac{33 - 7}{4})

Decimal Notation

- 3.18614 \dots < x < - 2.5 or - 2 < x < - 0.31385 \dots

Solution steps

∣ (x + 1) (x + 3) ∣ < \frac{x}{2} + 2

Find positive and negative intervals

x \leq - 3, - 3 < x < - 1, x \geq - 1

Solve the inequality for each interval

\frac{- 33 - 7}{4} < x \leq - 3 or (- 3 < x < - \frac{5}{2} or - 2 < x < - 1) or - 1 \leq x < \frac{33 - 7}{4}

Merge Overlapping Intervals

\frac{- 33 - 7}{4} < x < - \frac{5}{2} or - 2 < x < \frac{33 - 7}{4}

- 2 y > 40

3 n^{2} + 8 n - 3

(98 d)^{\frac{1}{2}}

x^{\frac{2}{5}}

- 4 x < - 13

What is |(x+1)(x+3)|< x/2+2 ?
The solution to |(x+1)(x+3)|< x/2+2 is (-sqrt(33)-7)/4 <x<-5/2 \lor-2<x<(sqrt(33)-7)/4