Suresh P. answered • 04/24/13

Friendly, patient tutor with experience in many subjects!

Hi Sage!

For the first one, we can rearrange the equation and add together common variables (i.e. all the x's) to make it look a little simpler. Since all the x's in this equation have the same exponent -- in this case, *no* exponent -- we can simply add 2x + 1x + 1x to get 4x. Since we cannot combine a "2" and a "4x" into one number, this is as far as we can simplify the left side.

Now we are left with 4x + 2 = -2. Moving the 2 over to the right side by subtracting it from each side, we get 4x = -4. Don't forget, a negative *minus* a positive (equivalent to *adding a negative*) gives you a more negative number. So, -2 - 2 = -4 (also, -2 + -2 = -4).

Now we can just divide each side by 4 to get rid of the coefficient in front of the x, and we're left with **x = -1**.

If we substitute -1 back in for x in the given equation, we can see that this is correct.

x + x + 2+ 2x = -2 --> (-1) + (-1) + 2 + 2(-1) = -2.

Suresh P.

04/24/13