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

• September 26th 2012, 08:45 AM
cocoa
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
• September 26th 2012, 08:52 AM
MarkFL
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:

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

Grouping like terms, we may write:

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

Combining the like terms, we find:

$-x+6=-2x-2$

Can you proceed from here?
• September 26th 2012, 09:15 AM
cocoa
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 ?
• September 26th 2012, 09:28 AM
MarkFL
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 $x=4$, we get:

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

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

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

$-18+20=-10$

$2=-10$

This is not true, so the solution is wrong.

We have:

$-x+6=-2x-2$

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

$-x+2x+6=-2x+2x-2$

Combining like terms, we find:

$x+6=-2$

Now subtract 6 from both sides, and you get:

$x+6-6=-2-6$

$x=-8$

Now, checking the solution:

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

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

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

$54-40=14$

$14=14$

This is true so we know the solution is correct.
• September 26th 2012, 10:22 AM
cocoa
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