<meta http-equiv="refresh" content="1; url=/nojavascript/"> Expressions with One or More Variables | CK-12 Foundation
Dismiss
Skip Navigation
You are reading an older version of this FlexBook® textbook: CK-12 Algebra I Concepts Go to the latest version.

1.2: Expressions with One or More Variables

Difficulty Level: At Grade Created by: CK-12
%
Best Score
Practice Expressions with One or More Variables
Practice
Best Score
%
Practice Now

What if the paycheck for your summer job were represented by the algebraic expression 10h + 25 , where h is the number of hours you work? If you worked 20 hours last week, how could you find the value of your paycheck? After completing this Concept, you'll be able to evaluate algebraic expressions like this one.

Watch This

CK-12 Foundation: 0102s evaluate algebraic expressions

Guidance

When we are given an algebraic expression, one of the most common things we might have to do with it is evaluate it for some given value of the variable. The following example illustrates this process.

Example A

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

Solution:

To find the solution, we substitute 12 for x in the given expression. Every time we see x , we replace it with 12.

2x - 7 &= 2(12) - 7\\&= 24 - 7\\&= 17

Note: At this stage of the problem, we place the substituted value in parentheses. We do this to make the written-out problem easier to follow, and to 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!)

Example B

Let y = -2. Find the value of  \frac {7} {y} - 11 y + 2 .

Solution

\frac {7} {(-2)} - 11( -2 ) + 2 &= -3 \frac { 1 } { 2 } + 22 + 2\\&= 24 - 3 \frac { 1 } { 2 }\\&= 20 \frac { 1 } { 2 }

Many expressions have more than one variable in them. For example, the formula for the perimeter of a rectangle in the introduction has two variables: length (l) and width (w) . In these cases, be careful to substitute the appropriate value in the appropriate place.

Example C

The area of a trapezoid is given by the equation  A = \frac{ h } { 2 } (a + b) . Find the area of a trapezoid with bases a = 10 \ cm and b = 15 \ cm and height h = 8 \ cm .

Solution:

To find the solution to this problem, we simply take the values given for the variables a, \ b, and h , and plug them in to the expression for A :

& A = \frac { h } { 2 }(a + b) \qquad \text{Substitute} \ 10 \ \text{for} \ a, \ 15 \ \text{for} \ b, \ \text{and} \ 8 \ \text{for} \ h.\\& A = \frac { 8 } { 2 }(10 + 15) \quad \text{Evaluate piece by piece.} \ 10 + 15 = 25; \ \frac { 8 } { 2 } = 4 .\\& A = 4(25) = 100

The area of the trapezoid is 100 square centimeters.

Watch this video for help with the Examples above.

CK-12 Foundation: Evaluate Algebraic Expressions

Vocabulary

  • When given an algebraic expression, one of the most common things we might have to do with it is evaluate it for some given value of the variable. We substitute the value in for the variable and simplify the expression.

Guided Practice

Let x= 3 and y = -2. Find the value of  3xy + \frac{6}{y}-2x .

Solution

3xy + \frac{6}{y}-2x &= 3(3)(-2) + \frac{6}{-2}-2(3)\\&= -18-3-6)\\&= -27

Practice

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

  1. 2a + 3b
  2. 4c + d
  3. 5ac - 2b
  4.  \frac { 2a } { c - d }
  5.  \frac { 3b } { d }
  6.  \frac { a - 4b } { 3c + 2d }
  7.  \frac { 1 } { a + b }
  8.  \frac { ab } {cd }

For 9-11, 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?

Image Attributions

Description

Difficulty Level:

At Grade

Sources:

Grades:

Date Created:

Sep 26, 2012

Last Modified:

Aug 21, 2014
Files can only be attached to the latest version of Modality

Reviews

Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.142.1.L.2

Original text