Solve −2(3x−5)−2x=2(6−3x). Show your work. Justify each step. Then check your solution.
Skip to input field
To solve the equation −2(3x−5)−2x=2(6−3x), we will first distribute the -2 and 2 on both sides of the equation.
Step 1: Distribute -2 on the left side of the equation
-2 * 3x = -6x
-2 * -5 = 10
So the left side of the equation becomes -6x + 10 - 2x = 2(6 - 3x)
Step 2: Distribute 2 on the right side of the equation
2 * 6 = 12
2 * -3x = -6x
So the right side of the equation becomes 12 - 6x
Now our equation becomes -6x + 10 - 2x = 12 - 6x
Step 3: Combine like terms on both sides of the equation
-6x - 2x + 10 = 12 - 6x
(-6x - 2x) on the left side becomes -8x
-6x - 6x on the right side becomes -12x
So our equation becomes -8x + 10 = 12 -12x
Step 4: Move all the x terms to one side of the equation
-8x + 12x = 12 - 10
-8x + 12x on the left side becomes 4x
So our equation becomes 4x = 2
Step 5: Solve for x by dividing both sides of the equation by 4
4x / 4 = 2 / 4
x = 1/2
To check our solution, we substitute x = 1/2 back into the original equation:
-2(3(1/2) - 5) - 2(1/2) = 2(6 - 3(1/2))
-2(3/2 - 5) - 2/2 = 2(6 - 3/2)
-2(-7/2) - 1 = 2(12/2 - 3/2)
14 - 1 = 2(9/2)
13 = 9
Since 13 is not equal to 9, our solution x = 1/2 is incorrect.