What is (12x+65)/((x+4)^2)>= 5 ?

The solution to (12x+65)/((x+4)^2)>= 5 is -5<= x<-4\lor-4<x<=-3/5

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(12x+65)/((x+4)^2)>= 5

\frac{12 x + 65}{( x + 4 ) ^{2}} \geq 5

- 5 \leq x < - 4 or - 4 < x \leq - \frac{3}{5}

Interval Notation

[- 5, - 4) \cup (- 4, - \frac{3}{5}]

Decimal Notation

- 5 \leq x < - 4 or - 4 < x \leq - 0.6

Solution steps

\frac{12 x + 65}{( x + 4 ) ^{2}} \geq 5

Rewrite in standard form

\frac{- 5 x ^{2} - 28 x - 15}{( x + 4 ) ^{2}} \geq 0

Factor

\frac{- 5 x ^{2} - 28 x - 15}{( x + 4 ) ^{2}} : \frac{- ( 5 x + 3 ) ( x + 5 )}{( x + 4 ) ^{2}}

\frac{- ( 5 x + 3 ) ( x + 5 )}{( x + 4 ) ^{2}} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 5 x + 3 ) ( x + 5 ) ) ( - 1 )}{( x + 4 ) ^{2}} \leq 0 \cdot (- 1)

Simplify

\frac{( 5 x + 3 ) ( x + 5 )}{( x + 4 ) ^{2}} \leq 0

Identify the intervals

- 5 \leq x < - 4 or - 4 < x \leq - \frac{3}{5}

(\frac{- 2}{2})^{2}

lo g_{3} (- 1)

(- \frac{2}{3})^{- 5}

1.6 x^{8}

∣ 3 - 2 x ∣ \geq - 7

What is (12x+65)/((x+4)^2)>= 5 ?
The solution to (12x+65)/((x+4)^2)>= 5 is -5<= x<-4\lor-4<x<=-3/5