Solving Equations using Addition and Subtraction.

To solve an equation means to find a value for the variable that makes the equation true. Whatever you do to one side of the equation, you must also do to the other side. An equation is like a balance scale because it shows that two quantities are equal. The scales remain balanced when the same weight is added to each side. Similarly, the scales remain balanced when the same weight is taken away from each side. This demonstrates the addition and subtraction properties of equality.

Addition Property of Equality

For every real number a, b, and c, if a = b, then a + c = b + c.

Subtraction Property of Equality

For every real number a, b, and c, if a = b, then a - c = b - c.

To solve an equation containing a variable, you find the value (or values) of the variable that make the equation true. Such a value is a solution of the equation. To find a solution, you can use properties of equality to form equivalent equations. Equivalent equations are equations that have the same solution (or solutions). We can solve equations with letters by getting rid of whatever is next to the letter on the left side of the equal sign so that the letter is on it's own. But we can't just get rid of what's on the left without doing the same thing to what's on the right of the equal sign.

One way to solve an equation is to get the variable alone on one side of the equal sign. You can do this using inverse operations, which are operations that undo one another. Addition and subtraction are inverse operations. When you solve an equation involving addition, subtract the same number from each side of the equation.

Solving Using Addition:

If the same number is added to each side of an equation, the resulting equation is equivalent to the original equation. In other words, adding same thing to each side of an equation does not change the equation.

Solving Using Subtraction:

If the same number is subtracted from each side of an equation, the resulting equation is equivalent to the original equation. In other words, subtracting same thing from each side of an equation does not change the equation.