2(x-3)-3(x+5)=3(x-2)-7
6x is this right
2x-6-3x-1=3x-6-7
-x-21=3x-13
-21=4x-13
-8=4x
-2=x
2(x-3)-3(x+5)=3(x-2)-7
2x - 6 -3x -15 = 3x - 6 -7
-4x = 8
x = -2
check
2(-2-3)-3(-2+5) =3(-2-2) -7 ?
-10 -9 = -12 -7
-19 = -19 sure enough
To solve the equation 2(x-3)-3(x+5)=3(x-2)-7, we need to simplify each side of the equation and then combine like terms.
First, let's distribute the multiplication on each side:
2(x-3) becomes 2x - 6
-3(x+5) becomes -3x - 15
3(x-2) becomes 3x - 6
Now our equation looks like this:
2x - 6 - 3x - 15 = 3x - 6 - 7
Next, combine like terms on each side of the equation:
On the left side, we have 2x - 3x = -x
On the right side, we have -6 - 15 = -21
On the right side, we also have -6 - 7 = -13
Now our equation looks like this:
-x - 21 = 3x - 13
To isolate the variable x, we need to get rid of the -x on the left side. We can do this by adding x to both sides of the equation:
-x + x - 21 = 3x - 13 + x
Simplifying further, we have:
-21 = 4x - 13
Now, let's isolate x by getting rid of the -13. We can do this by adding 13 to both sides of the equation:
-21 + 13 = 4x - 13 + 13
Simplifying further, we have:
-8 = 4x
To solve for x, divide both sides of the equation by 4:
-8/4 = 4x/4
Simplifying further, we have:
-2 = x
So the solution to the equation is x = -2.