What are the solutions to the inequality (x-3)(x+5) < _ 0

(x-3)(x-5)<_0

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.  

x−3=0x-3=0  

x+5=0x+5=0  

Set the first factor equal to 00 and solve.  

x=3x=3  

Set the next factor equal to 00 and solve.  

x=−5x=-5  

Consolidate the solutions.  

x=3,−5x=3,-5  

Use each root to create test intervals.  

x<−5x<-5  

−5<x<3-5<x<3  

x>3x>3  

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.  

x<−5x<-5 False  

−5<x<3-5<x<3 True  

x>3x>3 False  

The solution consists of all of the true intervals.  

−5<x<3-5<x<3  

The result can be shown in multiple forms.  

Inequality Form:  

−5<x<3-5<x<3  

Interval Notation:  

(−5,3)

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

answer: 100

step-by-step explanation: