# Algebraic Equations with two Variables

When we have an equation in 1 variable, with variables on 2 sides of the equation, again that means that there is only one variable (one letter), that is in more than one place (on both the left and right of the equal sign).

The goal is to get all the variables on one side of the equation and then to solve for the variable.

Here are some examples of what this might look like:

• 3x + 9 = 18x – 6
• 14b – 10 = 8b
• 4(w – 3) = 5w

The goal is to get all the variables on one side of the equation and then to solve for the variable.

The basic rule for grouping each term with the same variable, is to think about “doing the opposite.” You also want to look at which side of the equation is best to move the variable to, based on the signs of the other terms in the equation.

Let’s try one.

5x + 30 = 7x

First of all, there are “x’s” on both sides of the equation. The right side has a more x’s (7x versus 5x) so we will move the rest of the x’s to the right side. On the left side, the 5x is positive (+). When you have a positive term, “doing the opposite” is subtracting it.

We will subtract 5x from both sides of the equation:

(5x + 30) – 5x = (7x) – 5x

Group the terms with the variable on the left side:

(5x – 5x) + 30 = 7x – 5x

Now complete the subtraction:

30 = 2x

Now we can finish solving for x by dividing both sides by 2.

15 = x