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Question:

# Solve for x: 2(3x – 1) – 2(x + 5) = 12

A 6
explanation

When solving equations remember to use:
Inverse Operations – operations that undo one another. So if subtraction is present, we use addition, etc.
What we do to one side we MUST do to the other
Our goal is to ISOLATE the variable which means to have JUST one of the variables.
Step 1: Distribute
In this problem, we are first going to remove the parentheses from the equation. To do this we must multiply the term in front of each parenthesis by each term inside its respective parenthesis.
2(3x – 1) – 2(x + 5) = 12
6x – 2 – 2x – 10 = 12
Step 2: Combine Any Like Terms
Now we can rearrange the equation so that we can combine all whole numbers and all terms with the same variable. Also, remember to include the sign IN FRONT of each term.
6x – 2 – 2x – 10 = 12
If we rearrange, it becomes:
6x – 2x – 2 – 10 = 12
This simplifies to:
4x – 12 = 12
Step 3: Solve the Equation
When we solve equations, we can start by applying the inverse of the constant term on both sides of the equation. The constant is the term with no variable attached to it.
We see that 12 is being subtracted from 4x, the -12 is the constant term because there is no x attached, so we have to undo subtraction using addition. Therefore we are going to add 12 to both sides.
4x – 12 + 12 = 12 + 12
Which then becomes:
4x = 24
Now we can solve:
Since 4 is being multiplied by x, we have to undo the multiplication using division. Therefore we are going to divide both sides by 4.
(4x/4) = (24/4)
This simplifies to:
1x = 6
Since 1x and x are the same thing, our final answer is:
x = 6

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