# 1.2: Expressions with One or More Variables

**At Grade**Created by: CK-12

**Practice**Expressions with One or More Variables

### 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.

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Show More |

Term | Definition |
---|---|

algebraic |
The word algebraic indicates that a given expression or equation includes variables. |

Algebraic Expression |
An expression that has numbers, operations and variables, but no equals sign. |

Evaluate |
To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value. |

Exponent |
Exponents are used to describe the number of times that a term is multiplied by itself. |

Expression |
An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols. |

Order of Operations |
The order of operations specifies the order in which to perform each of multiple operations in an expression or equation. The order of operations is: P - parentheses, E - exponents, M/D - multiplication and division in order from left to right, A/S - addition and subtraction in order from left to right. |

Parentheses |
Parentheses "(" and ")" are used in algebraic expressions as grouping symbols. |

substitute |
In algebra, to substitute means to replace a variable or term with a specific value. |

Trapezoid |
A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides. |

### Image Attributions

Here you'll learn how to evaluate algebraic expressions by plugging in specific values for its variable(s).

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