4. Find the sum of (0.75x - 12y) and (-5 + 6y - 0.5x)

Show each step of your work.

5. Which expression(s) is/are equivalent to 8-2(5x-3). Show your work to justify your decision.

a. 6(5x-3)

b. 8-10x+6

c. 8-(10x-6)

d. 8-10x-6

e. -10x+14

6. In math class, students are attempting to simplify the expression written on the board: 7 - 2 (3 - 8x)

Three students make an attempt at a first step:

Len writes: 5 (3 - 8x)

Monty writes: 7 - 2 (-5x)

Nailany writes: 7 - 6 - 16x

Do you agree with any of the students? Explain your reasoning for each one.

yo i only got number 4 for you but here it goes: 0.70x+18y-5

Step-by-step explanation:

(0.75x  -  12y) + (-5  +  6y  -  0.5x)

regroup to the variables : (0.70x-0.5x) + (12y+ 6y-5)

put it together: (0.70x)+(18y-5)

you cant add unlike terms so you remove the parenthesies and your done.

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