this is as far as I got, not sure of the next step, group like terms but how?

-3(2x -2) +5x = -4x + 2(x-1)

-6 + 6 + 5x = -4x - 2x - 2

Re: this is as far as I got, not sure of the next step, group like terms but how?

Your first term on the left side should include *x*. Your second term on the right side should be positive. This gives you:

$\displaystyle -6x+6+5x=-4x+2x-2$

Grouping like terms, we may write:

$\displaystyle (5x-6x)+6=(2x-4x)-2$

Combining the like terms, we find:

$\displaystyle -x+6=-2x-2$

Can you proceed from here?

Re: this is as far as I got, not sure of the next step, group like terms but how?

is it ?

-2x -x = 6 -2

x = 4 ?

Re: this is as far as I got, not sure of the next step, group like terms but how?

No. If you are unsure about your solution, substitute it into the original equation to see if it satisfies the equation. For $\displaystyle x=4$, we get:

$\displaystyle -3(2(4)-2)+5(4)=-4(4)+2(4-1)$

$\displaystyle -3(8-2)+20=-16+2(3)$

$\displaystyle -3(6)+20=-16+6$

$\displaystyle -18+20=-10$

$\displaystyle 2=-10$

This is not true, so the solution is wrong.

We have:

$\displaystyle -x+6=-2x-2$

We may first add $\displaystyle 2x$ to both sides:

$\displaystyle -x+2x+6=-2x+2x-2$

Combining like terms, we find:

$\displaystyle x+6=-2$

Now subtract 6 from both sides, and you get:

$\displaystyle x+6-6=-2-6$

$\displaystyle x=-8$

Now, checking the solution:

$\displaystyle -3(2(-8)-2)+5(-8)=-4(-8)+2(-8-1)$

$\displaystyle -3(-16-2)-40=32+2(-9)$

$\displaystyle -3(-18)-40=32-18$

$\displaystyle 54-40=14$

$\displaystyle 14=14$

This is true so we know the solution is correct.

Re: this is as far as I got, not sure of the next step, group like terms but how?

wow thanks my issue is that I can't seem to get each step in the correct order I feel so lost but your technique is very very helpful. Again thanks