What is -x+5< 1/(x+3) ?

The solution to -x+5 1+sqrt(15)

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-x+5< 1/(x+3)

- x + 5 < \frac{1}{x + 3}

- 3 < x < 1 - 15 or x > 1 + 15

Interval Notation

(- 3, 1 - 15) \cup (1 + 15, \infty)

Decimal Notation

- 3 < x < - 2.87298 \dots or x > 4.87298 \dots

Solution steps

- x + 5 < \frac{1}{x + 3}

Rewrite in standard form

\frac{- x ^{2} + 2 x + 14}{x + 3} < 0

Factor

- x^{2} + 2 x + 14 : - (x - 1 - 15) (x - 1 + 15)

\frac{- ( x - 1 - 15 ) ( x - 1 + 15 )}{x + 3} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 - 15 ) ( x - 1 + 15 ) ) ( - 1 )}{x + 3} > 0 \cdot (- 1)

Simplify

\frac{( x - 1 - 15 ) ( x - 1 + 15 )}{x + 3} > 0

Identify the intervals

- 3 < x < 1 - 15 or x > 1 + 15

z^{2} - 4 z + 4

\frac{x}{4} < 5

y^{4} - 5 y^{2} - 36

(0.014438) t^{2} + t - 3 = 0

10 - 0.2 x = 9.1

What is -x+5< 1/(x+3) ?
The solution to -x+5< 1/(x+3) is -3<x<1-sqrt(15)\lor x>1+sqrt(15)