Solving Equations with variables

An equation is like a balance scale because it shows that 2 quantities are equal. To solve an equation containing a variable, you find the value of the variable that makes the equation true. This type of value is a solution of the equation. To find out the solution, you can use properties of equality to form equivalent equations. Equivalent equations are equations which are having the same solution. We can solve equations with letters by getting rid of whatever is next to the letter on left side of the equal sign so that the letter is on its own. But we cannot get rid of what's on the left without doing the same thing to what's on the right of the equal sign.

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 means to find a value for the variable which makes the equation true. Whatever you do to one side of the equation, you should also do to the other side. One way to solve the equation is to get variable on one side alone of the equal sign. We can do this by using inverse operation, which are operations which undo one another. Subtraction and Addition are inverse operations. When you solve the equation which involves addition, subtract the same number from each side of the equation.

Solving Using Addition:

If the same number is added on each side of an equation, the resulting equation is equivalent to the original equation. Or we can say that 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 the equation, resulting equation is equivalent to the original equation. Or we can say that, subtracting same thing from each side of an equation does not change the equation.

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