<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

1.2: Expressions with One or More Variables

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Estimated15 minsto complete
%
Progress
Practice Expressions with One or More Variables
Practice
Progress
Estimated15 minsto complete
%
Practice Now
Turn In

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 x in the given expression.

2x7=2(12)7=247=17

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 "2x" into "212" instead of "2 times 12!")

Evaluating an Expression 

Let y=2. Find the value of 7y11y+2.

7(2)11(2)+2=312+22+2=24312=2012

Many expressions have more than one variable in them. For example, the formula for the perimeter of a rectangle, P=2l+2w, has two variables: length (l) and width (w). 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 A=h2(a+b). Find the area of a trapezoid with bases a=10 cm and b=15 cm and height h=8 cm.

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

AA=h2(a+b) Substitute 10 for a, 15 for b, and 8 for h.=(8)2((10)+(15))Evaluate piece by piece. 10+15=25 and 82=4.=4(25)=100

Example

Example 1

Let x=3 and y=2. Find the value of 3xy+6y2x.

3xy+6y2x=3(3)(2)+6(2)2(3)=(18)+(3)(6)=27

Review 

Evaluate questions 1 through 8, using a=3, b=2, c=5, and d=4.

  1. 2a+3b
  2. 4c+d
  3. 5ac2b
  4. 2acd
  5. 3bd
  6. a4b3c+2d
  7. 1a+b
  8. abcd

For questions 9 through 11, the weekly cost C of manufacturing x remote controls is given by the formula C=2000+3x, where the cost is given in dollars.

  1. What is the cost of producing 1000 remote controls?
  2. What is the cost of producing 2000 remote controls?
  3. 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

Vocabulary

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

Show Hide Details
Description
Difficulty Level:
At Grade
Sources:
Grades:
Date Created:
Sep 26, 2012
Last Modified:
Apr 11, 2016
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the Modality. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.142.1.L.2
Here