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91
2.4
Solving an Equation
P
urpose
The role this topic plays in quantitative reasoning
You can solve some equations that arise in the real world by isolating a variable. You can use this method
to solve the following equation
1
400 1 (10) 460
2
x
+
=
in order to determine the number of hours of overtime you need to work to earn $460 per week, at an
hourly rate of $10, with overtime being paid at “time and a half.”
Isolating a variable to solve an equation is probably one of the three most common quantitative reasoning
tasks you are likely to encounter in your other courses. And knowing how to validate that your equation
solutions are correct truly can help you raise your exam scores because you will only submit answer that
you know are correct!
L
earning Goals
What you should learn while completing this activity
1. Solve a linear equation using the Isolate the Variable Methodology
2. Solve a literal equation
3. Use the Solving Linear Equations Methodology to find the solution to a linear equation involving
fractions and parentheses
D
iscovery
Finding out for yourself
How many cell phone batteries can you buy from the battery store online? You know the shipping will
be $8 and each battery costs $3.50 and you have $20 available. How many batteries can you buy? Is
this a common problem? What about determining how much food, such as pizzas, you should buy for
a party? Or how many movies you can afford to pay to see each month? Every time you have a limit to
how much you can spend spend or invest and want to determine quantities that you can afford to buy or
invest in, how do you do it effectively?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. Give two examples of pairs of equivalent equations.
2. Use the Addition Property of Equality to create an equation that is equivalent to 6 3 5
x
+ =
.
3. Use the Multiplication Property of Equality to create an equation that is equivalent to 3( 5) 6
x
− − =
.
4. Use the Distributive Property and the Substitution Principle to create an equation that is equivalent
to 5 2(3 ) 10
x
x
+ − =
.