What is 7+(25)/(x-4)>= 4/(x+3) ?

The solution to 7+(25)/(x-4)>= 4/(x+3) is x 4

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7+(25)/(x-4)>= 4/(x+3)

7 + \frac{25}{x - 4} \geq \frac{4}{x + 3}

x < - 3 or x = - 1 or x > 4

Interval Notation

(- \infty, - 3) \cup x = - 1 \cup (4, \infty)

Solution steps

7 + \frac{25}{x - 4} \geq \frac{4}{x + 3}

Rewrite in standard form

\frac{7 x ^{2} + 14 x + 7}{( x - 4 ) ( x + 3 )} \geq 0

Factor

\frac{7 x ^{2} + 14 x + 7}{( x - 4 ) ( x + 3 )} : \frac{7 ( x + 1 ) ^{2}}{( x - 4 ) ( x + 3 )}

\frac{7 ( x + 1 ) ^{2}}{( x - 4 ) ( x + 3 )} \geq 0

Divide both sides by

7

\frac{\frac{7 ( x + 1 ) ^{2}}{( x - 4 ) ( x + 3 )}}{7} \geq \frac{0}{7}

Simplify

\frac{( x + 1 ) ^{2}}{( x - 4 ) ( x + 3 )} \geq 0

Identify the intervals

x < - 3 or x = - 1 or x > 4

x - 11 \leq 0

x^{3} + 9 x^{2} - x \geq 9

w^{3} - 27

2 x - 1 = 3 (2 x + 2) - 4

\frac{1}{2} \cdot \frac{4}{1}

What is 7+(25)/(x-4)>= 4/(x+3) ?
The solution to 7+(25)/(x-4)>= 4/(x+3) is x<-3\lor x=-1\lor x>4