1.2: Expressions with One or More Variables
What if the paycheck for your summer job were represented by the algebraic expression \begin{align*}10h + 25\end{align*}
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CK12 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 \begin{align*}x = 12\end{align*}
Solution:
To find the solution, we substitute 12 for \begin{align*}x\end{align*}
\begin{align*}2x  7 &= 2(12)  7\\ &= 24  7\\ &= 17\end{align*}
Note: At this stage of the problem, we place the substituted value in parentheses. We do this to make the writtenout 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 \begin{align*}2x\end{align*}
Example B
Let \begin{align*}y = 2. \end{align*}
Solution
\begin{align*}\frac {7} {(2)}  11( 2 ) + 2 &= 3 \frac { 1 } { 2 } + 22 + 2\\ &= 24  3 \frac { 1 } { 2 }\\ &= 20 \frac { 1 } { 2 }\end{align*}
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 \begin{align*}(l)\end{align*}
Example C
The area of a trapezoid is given by the equation \begin{align*} A = \frac{ h } { 2 } (a + b)\end{align*}
Solution:
To find the solution to this problem, we simply take the values given for the variables \begin{align*}a, \ b,\end{align*}
\begin{align*}& 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\end{align*}
The area of the trapezoid is 100 square centimeters.
Watch this video for help with the Examples above.
CK12 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 \begin{align*}x= 3\end{align*}
Solution
\begin{align*}3xy + \frac{6}{y}2x &= 3(3)(2) + \frac{6}{2}2(3)\\ &= 1836)\\ &= 27\end{align*}
Practice
Evaluate 18 using \begin{align*}a = 3, \ b = 2, \ c = 5,\end{align*}

\begin{align*}2a + 3b\end{align*}
2a+3b 
\begin{align*}4c + d\end{align*}
4c+d 
\begin{align*}5ac  2b\end{align*}
5ac−2b 
\begin{align*} \frac { 2a } { c  d }\end{align*}
2ac−d 
\begin{align*} \frac { 3b } { d }\end{align*}
3bd 
\begin{align*} \frac { a  4b } { 3c + 2d }\end{align*}
a−4b3c+2d 
\begin{align*} \frac { 1 } { a + b }\end{align*}
1a+b 
\begin{align*} \frac { ab } {cd }\end{align*}
abcd
For 911, the weekly cost \begin{align*}C\end{align*}
 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?
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
Description
Learning Objectives
Here you'll learn how to evaluate algebraic expressions by plugging in specific values for its variable(s).