2(x-3)-3(x+5) = 3(x-2)-7
I will be happy to critique your work.
2(x-3) - 3(x+5) = 3(x-2)-7
2x - 6 - 3x + 15 = 3x - 6 - 7
2x - 6 + 6 - 3x +15 + 6 = 3x - 6 - 7
2x - 3x + 22 = 3x - 7
2x + 22 = -7
Now I am stuck
I see a problem with your second line. When you distributed the -3 into (x+5), you forgot your negative: (-3)(5) = -15.
2(x-3) - 3(x+5) = 3(x-2) -7
(2x-6) - 3x+-15 = (3x-6) -7
-x-21 = 3x-13
-x-3x = -13+21
-4x = 8
x = 8/-4
x = -2
Is this correct?
To solve this equation, you need to simplify both sides and then isolate the variable.
Let's start by simplifying each side of the equation step by step:
1. Distribute the coefficients inside the parentheses on both sides:
2(x-3) - 3(x+5) = 3(x-2) - 7
2x - 6 - 3x - 15 = 3x - 6 - 7
2. Combine like terms on each side:
2x - 3x - 6 - 15 = 3x - 6 - 7
-x - 21 = 3x - 13
3. Move all terms containing x to one side by adding x to both sides:
-x + x - 21 = 3x - x - 13
-21 = 2x - 13
4. Move the constant term to the other side by adding 21 to both sides:
-21 + 21 = 2x - 13 + 21
0 = 2x + 8
5. Divide both sides by 2 to isolate x:
0/2 = (2x + 8) / 2
0 = x + 4
Therefore, the solution to the equation 2(x-3) - 3(x+5) = 3(x-2) - 7 is x = -4.