Your summer landscaping job pays a fixed rate of $20 per job plus $4 an hour. How much total money would you would make if it takes you 3 hours to complete a single job?
Watch This
Khan Academy: Variables Expressions and Equations
Guidance
You have probably seen letters in a mathematical expression, such as . These letters, also called variables, represent an unknown number. One of the goals of algebra is to solve various equations for a variable. Typically, is used to represent the unknown number, but any letter can be used.
To evaluate an expression or equation, we would need to substitute in a given value for the variable and test it. In order for the given value to be true for an equation, the two sides of the equation must simplify to the same number.
Example A
Evaluate for .
Solution: We know that is an expression because it does not have an equals sign. Therefore, to evaluate this expression, plug in -3 for and simplify using the Order of Operations.
You will need to remember that when squaring a negative number, the answer will always be positive. There are three different ways to write multiplication: , and 2(9).
Example B
Determine if is a solution to .
Solution: Even though the directions are different, this problem is almost identical to Example A. However, this is an equation because of the equals sign. Both sides of an equation must be equal to each other in order for it to be true. Plug in 5 everywhere there is an . Then, determine if both sides are the same.
Because , this is not a true equation. Therefore, 5 is not a solution.
Example C
Determine if is a solution to .
Solution: Here, is the variable and it is listed twice in this equation. Plug in -2 everywhere there is a and simplify.
-2 is a solution to this equation.
Intro Problem Revisit Rewrite the sentence as an algebraic expression. $20 plus $4 an hour, would be , where h equals the number of hours you work. Then, evaluate the expression for .
You will make a total of $32 for this particular job.
Guided Practice
1. Evaluate for .
2. Determine if is a solution to .
Answers
1. Plug in 4 everywhere there is an .
2. Plug in -1 for and see if both sides of the equation are the same.
Because the two sides are not equal, -1 is not a solution to this equation.
Vocabulary
- Variable
- A letter used to represent an unknown value.
- Expression
- A group of variables, numbers, and operators.
- Equation
- Two expressions joined by an equal sign.
- Solution
- A numeric value that makes an equation true.
Practice
Evaluate the following expressions for .
Evaluate the following expressions for the given value.
Determine if the given values are solutions to the equations below.
Find the value of each expression, given that , and .
For problems 20-25, use the equation .
- Is a solution to this equation?
- Is a solution to this equation?
- Is a solution to this equation?
- Is a solution to this equation?
- Do you think there are any other solutions to this equation, other than the ones found above?
- Challenge Using the solutions you found from problems 20-23, find the sum of these solutions and their product. What do you notice?