the first one is: x+x+2+2x=-2

the second one is: 3x-9x+7-3=-8

the first one is: x+x+2+2x=-2

the second one is: 3x-9x+7-3=-8

Tutors, please sign in to answer this question.

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.

To understand how this works you need to know two things

a) that x is just like another number

b) what = means

= means that what is on the left side of the equation is EQUAL to what is on the right side of the equation

So to be true to what EQUAL means, whatever you do to the left side you have to do to the right side

I'm going to use * to mean multiply since x means something other than multiply here.

so for x + x + 2 + 2 * x = -2

it's like a puzzle, get just x on one side of the = sign and you win

Since all the x's are already on the left, let's round them up

1 * x + 1 *x + 2*x + 2 = -2

so if I had 1 apple + 1 apple + 2 apples how many apples is that?

4 * x + 2 = -2

Next we want to get rid of the 2 on the left side, so SUBTRACT 2 from both sides

4 * x + 2 - 2 = - 2 - 2

4 * x = - 4

Finally we want to get rid of the 4 in front of the x, so divide both sides by 4

4 * x/4 = -4/4

x = -1

The other problem you should do yourself.

## Comments