### Multiple Variable Expressions

When given an algebraic expression, one of the most common things to do with it is **evaluate** it for some given value of the variable.

Take a look at this example to see how this works:

Let x = 12. Find the value of 2x - 7.

To find the solution, substitute 12 in place of in the given expression.

**Note:** In the first step of the problem, keep the substituted value in parentheses. This makes the written-out problem easier to follow, and helps avoid mistakes. (If we didn’t use parentheses and also forgot to add a multiplication sign, we would end up turning "" into "212" instead of "2 *times* 12!")

#### Evaluating an Expression

Let Find the value of

Many expressions have more than one variable in them. For example, the formula for the perimeter of a rectangle, , has two variables: length and width Be careful to substitute the appropriate value in the appropriate place.

#### Evaluating an Expression with Multiple Variables

The area of a trapezoid is given by the equation . Find the area of a trapezoid with bases and and height .

To find the solution to this problem, substitute the given values for variables and in place of the appropriate letters in the equation.

### Example

#### Example 1

Let and Find the value of .

### Review

Evaluate questions 1 through 8, using and

For questions 9 through 11, the weekly cost of manufacturing remote controls is given by the formula , where the cost is given in dollars.

- What is the cost of producing 1000 remote controls?
- What is the cost of producing 2000 remote controls?
- What is the cost of producing 2500 remote controls?

### Review (Answers)

To view the Review answers, open this PDF file and look for section 1.2.