Double-sided equations can be solved by doing the same operation to both sides of the equals sign. This keeps the equation balanced. Terms should be combined so that variables are grouped together on one side and constants on the other. When a term crosses the equals sign to the other side, its sign changes. By following these steps, variables can be isolated so the equation can be solved.

1. Double-Sided Equations

2. An equals sign (=) means that the two sides have the same value 2x – 5 6x + 7 =

3. Whatever you do to one side, you must do to the other If you only do something to one side, then the equation becomes unbalanced, like the picture above

4. You want to get the same types of things together  the variables with the variables, and the constants with the constants Notice how the arrows kind of make a circle 2x – 5 6x + 7 =

5. When you take the “6x” across the equals sign , it has to change signs Quick note for remembering: Crossing the sign changes the sign 2x – 5 -6x 6x + 7 =

6. Now we can take the – 5 across to the 7. Remember that crossing the equals sign changes the sign – 4x– 5 7 = + 5

7. Now, the variable has to be completely by itself. Divide by – 4. – 4x – 4 12 – 4 =

8. You are finished! x – 3 =