Quandaries and Queries


Hi my name is Angela and I am in High School. I not going to give you the problem that I have, but a problem like it.

4(r-2) = r(2+8)

I get mix up trying to solve a problem like this could you help me. So that I will be able to handle the ones on my homework.



Hi Angela,

Look at the right side of this equation, r(2+8). There are two ways I can evaluate this expression.

    1. Add 2+8 and then multiply by r.
      r(2+8) = r(10) = 10r

    2. Multiply by r first, and then add
      r(2+8) = r2 + r8 = 2r + 8r = 10r

On the left side, r - 2 can't be simplified further so option 1 above isn't available. I can, however expand the left side as I did in the second option

4(r - 2) = 4r - 42 = 4r - 8

Thus your equation is

4(r - 2) = r(2 + 8)
4r - 8 = 10r

The goal is to "solve for r", that is to manipulate this equation to put it in the form

r = "number"

I don't want an r on both sides and I can accomplish that by adding -4r to both sides

4r - 8 = 10r
-4r + 4r - 8 = 10 - 4r
-8 = 6r

Now divide both sides by 6

  -4/3 = r

Thus r = -4/3



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