solve for x:
2(x-3) - 3(x+5) = 3 (x-2) - 7
Perform the indicated multiplications; add up the constants and the terms that involve x; then get all terms that involve x on one side of the equation.
2x -6 -3x -15 = 3x -6 -7
-x -21 = 3x -13
-8 = 4x
x = ?
-2
To solve for x in the equation 2(x-3) - 3(x+5) = 3(x-2) - 7, follow these steps:
Step 1: Distribute the coefficients:
2(x-3) = 2x - 6
-3(x+5) = -3x - 15
3(x-2) = 3x - 6
So, the equation becomes:
2x - 6 - 3x - 15 = 3x - 6 - 7
Step 2: Combine like terms on both sides of the equation:
(2x - 3x) + (-6 - 15) = (3x - 6 - 7)
Simplifying:
-x - 21 = 3x - 13
Step 3: Bring all the terms involving x to one side of the equation by adding x to both sides:
(-x - 21) + x = (3x - 13) + x
Simplifying:
-21 = 4x - 13
Step 4: Move the constant term to the other side of the equation by subtracting 13 from both sides:
-21 + 13 = 4x - 13 - 13
Simplifying:
-8 = 4x
Step 5: Solve for x by dividing both sides of the equation by 4:
(-8) / 4 = (4x) / 4
Simplifying:
x = -2
Therefore, the solution to the equation is x = -2.