Solve the inequality for x: -3(2x+5) < -45

x>5

Step-by-step explanation:

-3(2x+5)<-45

2x+5<-45/-3

2x+5<15

2x<15-5

2x<10

x<10/2

x<5

x>5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4