- Match each equation with an equivalent equation. Some of the answer choices are not used.
A. 3x + 6 = 4x + 7
1.9x = 4x + 7
B. 3(x + 6) = 4x +7
2. 3x + 18 = 4x + 7
C. 4x + 3x = 7-6
3. 3x = 4x + 7
4. 3x - 1 = 4x
5. 7x = 1

A,4-B,2-C,5

Solution:

If you need to show the work just try to do it until you get the right answers because it helps you actually learn how to do it=_=

A. X=-1

B. X=11

C. X=1/7

1. X=7/5

2. X=11

3. X=-7

4. X=-1

5. X=1/7

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