Expert: Scott A Wilson - 2/16/2011

Question
Ive been doin some mathalgebra problems and i came across 2 of which i couldnt solve

10 + 2x = 5x - 5

and

2t + 8 = 4t -5 - t

Answer
For the 1st one, subtract 2x from both sides and add 5 to both sides.
That is, add 5 - 2x to both sides of the equation.

This gives 10 + 2x + 5 - 2x = 5x - 5 + 5 - 2x.
On the left, 2x - 2x = 0 and on the right, -5 + 5 = 0.
On the left, 10 + 5 = 15 and on the right, 5x - 2x = 3x.
This gives 15 = 3x, so x = 5.

Putting this back in gives 10 + 2(5) = 5(5) - 5, and both sides can be seen to be 20.

For 2t + 8 = 4t - 5 - t, on the right we have 4t - t = 3t, so it is
2t + 8 = 3t - 5.

Another way to do these is to note that the right sides has one more t,
but -5 is 13 less than 8, so t = 13.

Putting that back in gives 2(13) + 8 = 3(13) - 5, and both sides are 34.