M1V1i + M2V2i = (M1 + M2)Vf ... How do I isolate M2

I'm not the best at rearranging equations and I don't know how to isolate for mass 2 if you have it on both sides
Show work plzz 10 points best answer thanks

Hmm, let's see, well we can divide both sides by Vf to get that M2 on the right side out of parentheses.

(M1V1i + M2V2i)/Vf = M1 + M2

No, that didn't really help. Now there's an M2 in parentheses on the left, so we didn't really advance any. Let's try a different approach. Use the distributive law to get rid of the parentheses on the right.

M1V1i + M2V2i = M1Vf + M2Vf

Now let's just add and subtract things to both sides to get terms with M2 on one side.

1) -M1V1i

M2V2i = M1Vf + M2Vf - M1V1i

2) -M2Vf

M2V2i - M2Vf = M1Vf - M1V1i

Great ok, every term on the left has M2. So you can use reverse distributive law.

M2(V2i - Vf) = M1Vf - M1V1i

Now it's easy to divide both sides by the parentheses on the left.

M2 = (M1Vf - M1V1i)/(V2i - Vf)

Problem solved. However to make it prettier, you can distribute out M1 from the right hand side.

M2 = M1(Vf - V1i)/(V2i - Vf)

I showed you the first misstep so hopefully you can see not only the way to solve the problem, but the way to think about rearranging equations. Know all the transformations you can apply, and try them and see if they seem to be getting you closer to your goal.

Given:
M1*V1i + M2*V2i = (M1 + M2)*Vf

Expand:
M1*V1i + M2*V2i = M1*Vf + M2*Vf

Gather the M1 terms to the left side by subtracting M1*Vf from both sides:
M1*V1i - M1*Vf + M2*V2i = M2*Vf

Subtract M2*V2i from both sides:
M1*V1i - M1*Vf = M2*Vf - M2*V2i


Factor:
M1*(V1i - Vf) = M2*(Vf - V2i)

Divide and isolate:
M2 = M1*(V1i - Vf)/(Vf - V2i)