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Popular >

(x+38)/(x+6)<5

Solution

\frac{x + 38}{x + 6} < 5

Solution

x < - 6 or x > 2

+1

Interval Notation

(- \infty, - 6) \cup (2, \infty)

Solution steps

\frac{x + 38}{x + 6} < 5

Rewrite in standard form

\frac{- 4 x + 8}{x + 6} < 0

Factor

\frac{- 4 x + 8}{x + 6} : \frac{- 4 ( x - 2 )}{x + 6}

\frac{- 4 ( x - 2 )}{x + 6} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 4 ( x - 2 ) ) ( - 1 )}{x + 6} > 0 \cdot (- 1)

Simplify

\frac{4 ( x - 2 )}{x + 6} > 0

Divide both sides by

4

\frac{\frac{4 ( x - 2 )}{x + 6}}{4} > \frac{0}{4}

Simplify

\frac{x - 2}{x + 6} > 0

Identify the intervals

x < - 6 or x > 2

Popular Examples

3 x^{2} = 1 0^{8}

8 (b + 3) = 4 b - 4

factor 2x^3-4x^2+2x factor

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

(x-4)(x+7)=(x-4)(x+7)

(x - 4) (x + 7) = (x - 4) (x + 7)

x^{2} - x + 6 = 0

Frequently Asked Questions (FAQ)

What is (x+38)/(x+6)<5 ?
The solution to (x+38)/(x+6)<5 is x<-6\lor x>2