## Monday, November 12, 2007

### Solving Inequalities

Another type of sentence used in algebra is called an inequality.

An inequality is used when we don't know exactly what an expression is equal to.

In order to solve an inequality, we have to combine like terms like you would if you were solving an equation.

For example, if you are asked to solve for x in the following equation: 5x + 3 = 13, you all know that you had to subtract 3 from both sides of the equation because our goal is to get x by itself and also because we know we have to do the inverse operation. In this case, the inverse of addition is subtraction.

After you subtracted 3 from both sides of the equation, you should have been left with 5x = 10. We have to get 5 from x because again, our goal is to get x by itself. Because we know that 5x is really 5 times x, we know that we have to do the inverse of multiplication to get x alone. So, we divide both sides by 5. Then, we are left with x = 10.

We use the same skills we use to solve equations to solve inequalities. We have to remember that our goal is to end up with a variable on one side of the inequality and a value on the other side.