What is [((x+3))/((x+8))]>= 6 ?

The solution to [((x+3))/((x+8))]>= 6 is -9<= x<-8

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[((x+3))/((x+8))]>= 6

[\frac{( x + 3 )}{( x + 8 )}] \geq 6

- 9 \leq x < - 8

Interval Notation

[- 9, - 8)

Solution steps

[\frac{x + 3}{x + 8}] \geq 6

Rewrite in standard form

\frac{- 5 x - 45}{x + 8} \geq 0

Factor

\frac{- 5 x - 45}{x + 8} : \frac{- 5 ( x + 9 )}{x + 8}

\frac{- 5 ( x + 9 )}{x + 8} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 5 ( x + 9 ) ) ( - 1 )}{x + 8} \leq 0 \cdot (- 1)

Simplify

\frac{5 ( x + 9 )}{x + 8} \leq 0

Divide both sides by

5

\frac{\frac{5 ( x + 9 )}{x + 8}}{5} \leq \frac{0}{5}

Simplify

\frac{x + 9}{x + 8} \leq 0

Identify the intervals

- 9 \leq x < - 8

19 - 3 x \leq - (1 + 7 x)

- (a + 1) - 4 a \leq 2 a - 8

- \frac{6}{1}

2 a - 4

(\frac{3 m ^{- 5} n ^{2}}{4 m ^{- 2} n ^{0}})^{2} \cdot (\frac{m n ^{4}}{9 n})^{2}

What is [((x+3))/((x+8))]>= 6 ?
The solution to [((x+3))/((x+8))]>= 6 is -9<= x<-8