3.2: One-Step Equations Transformed by Multiplication/Division
What if you had an algebraic equation involving multiplication or division like ? How could you solve it for the unknown variable x ? After completing this Concept, you'll be able to solve equations like this one.
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CK-12 Foundation: 0302S Solving Equations with Multiplication and Division (H264)
Guidance
Suppose you are selling pizza for $1.50 a slice and you can get eight slices out of a single pizza. How much money do you get for a single pizza? It shouldn’t take you long to figure out that you get . You solved this problem by multiplying. Here’s how to do the same thing algebraically, using to stand for the cost in dollars of the whole pizza.
Example A
Solve .
Our is being multiplied by one-eighth. To cancel that out and get by itself, we have to multiply by the reciprocal, 8. Don’t forget to multiply both sides of the equation.
Example B
Solve .
0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4.
Solving by division is another way to isolate . Suppose you buy five identical candy bars, and you are charged $3.25. How much did each candy bar cost? You might just divide $3.25 by 5, but let’s see how this problem looks in algebra.
Example C
Solve .
To cancel the 5, we divide both sides by 5.
Example D
Solve .
Divide by 1.375
Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272....
To see more examples of one - and two-step equation solving, watch the Khan Academy video series starting at http://www.youtube.com/watch?v=bAerID24QJ0 .
Watch this video for help with the Examples above.
CK-12 Foundation: Solving Equations with Multiplication and Division
Vocabulary
- An equation in which each term is either a constant or the product of a constant and a single variable is a linear equation .
- We can add, subtract, multiply, or divide both sides of an equation by the same value and still have an equivalent equation .
- To solve an equation, isolate the unknown variable on one side of the equation by applying one or more arithmetic operations to both sides.
Guided Practice
Solve:
a) .
b) .
Solutions:
a) is equivalent to , so to cancel out that , we multiply by the reciprocal, .
b) Divide both sides by 7.
Practice
For 1-5, solve the following equations for .
For 6-10, solve the following equations for the unknown variable.
Image Attributions
Description
Learning Objectives
Here you'll learn how to use multiplication and division to solve algebraic equations for their unknown variable.