Lloyd solves the equation 24x + 18(x – 2) = 216 for x. Some of his steps are shown. Step 1: 24x + 18(x – 2) = 216

Step 2: 24x + 18x – 36 = 216

Step 3: 42x – 36 = 216

Step 4: 42x = 252

Which of the following statements BEST describes what Lloyd did to get from Step 3 to Step 4?

Hi there!

Your answer is:

To get from step 3 to step 4, Lloyd added 36 to both sides. On the left side, this equaled 0 due to the additive inverse property! (-36 + 36 = 0!) On the right side, 36 is added to 216! (216+36 = 252)

5

step-by-step explanation:

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