1.4: Single Variable Expressions
Shelly is making bracelets to sell at her town's market this summer. She spent $150 on supplies and will make $4 for every bracelet she sells. Her profit for selling
In this concept, you will learn how to evaluate single variable expressions.
Evaluating Single Variable Expressions
An expression is a mathematical phrase that contains numbers and operations.
Here are some examples of expressions:

3x+10 −15+7−1 52−1 
15r+2
A variable is a symbol or letter (such as
Here are some examples of variable expressions:
3x+10 10r b3+2 mx−3
A single variable expression is a variable expression with just one variable in it.
You can use a variable expression to describe a real world situation where one or more quantities has an unknown value or can change in value.
To evaluate a variable expression means to find the value of the expression for a given value of the variable. To evaluate, substitute the given value for the variable in the expression and simplify using the order of operations. To follow the order of operations, you always need to do any multiplication/division first before any addition/subtraction.
Here is an example.
Evaluate the expression
First, remember that when you see a number next to a letter, like “
Next, substitute 12 in for the letter
Notice that you can put parentheses around the 12 to keep it separate from the number 10.
Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
The answer is 76.
Here is another example that involves division.
Evaluate the expression
First, remember that a fraction bar is like a division sign.
Next, substitute 24 in for the letter
Now, simplify the expression using the order of operations. You will need to divide first and then add.
The answer is 10.
Examples
Example 1
Earlier, you were given a problem about Shelly and her bracelet business.
Shelly is selling bracelets this summer and her profit for selling
To calculate her profit from selling 50 bracelets, Shelly needs to evaluate the expression
First, substitute 50 in for the letter
Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
Shelly's profit from selling 50 bracelets would be $50.
Example 2
Evaluate
First, substitute 49 in for the letter
Now, simplify the expression using the order of operations. You will need to divide first and then subtract.
The answer is 2.
Example 3
Evaluate
First, substitute 20 in for the letter
Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
The answer is 71.
Example 4
Evaluate
First, substitute 9 in for the letter
Now, simplify the expression using the order of operations. You will need to multiply first and then add.
The answer is 51.
Example 5
Evaluate
First, substitute 36 in for the letter
\begin{align*}\frac{36}{4}8\end{align*}
Now, simplify the expression using the order of operations. You will need to divide first and then subtract.
\begin{align*}\begin{array}{rcl} \frac{36}{4}8 &=& 98\\ &=& 1 \end{array}\end{align*}
The answer is 1.
Review
Evaluate each expression if the given value of \begin{align*}r\end{align*} is 9.
 \begin{align*}\frac{r}{3}\end{align*}
 \begin{align*}63  r\end{align*}
 \begin{align*}11r\end{align*}
 \begin{align*}2r + 7\end{align*}
 \begin{align*}3r + r\end{align*}
 \begin{align*}4r  2r\end{align*}
 \begin{align*}r + 5r\end{align*}
 \begin{align*}12r  1\end{align*}
Evaluate each expression for \begin{align*}h=12\end{align*}.
 \begin{align*}70  3h\end{align*}
 \begin{align*}6h + 6\end{align*}
 \begin{align*}4h  9\end{align*}
 \begin{align*}11 + \frac{h}{4}\end{align*}
 \begin{align*}3h + h\end{align*}
 \begin{align*}2h + 5h\end{align*}
 \begin{align*}6h  2h\end{align*}
Review (Answers)
To see the Review answers, open this PDF file and look for section 1.4.
Resources
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In this concept, you will learn how to evaluate single variable expressions.
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