What is |x^2+4x+3|>x+3 ?

The solution to |x^2+4x+3|>x+3 is x 0

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|x^2+4x+3|>x+3

x^{2} + 4 x + 3 > x + 3

x < - 3 or - 3 < x < - 2 or x > 0

Interval Notation

(- \infty, - 3) \cup (- 3, - 2) \cup (0, \infty)

Solution steps

x^{2} + 4 x + 3 > x + 3

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 3 or - 3 < x < - 2 or x > 0

∣ x ∣ + x^{2} > 0

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

∣ 3 x + 5 ∣ \leq \frac{7}{2}

\frac{1}{∣ x - 2 ∣} > 2

\frac{3 x}{x ^{2} - 4} \leq 1

What is |x^2+4x+3|>x+3 ?
The solution to |x^2+4x+3|>x+3 is x<-3\lor-3<x<-2\lor x>0