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One-Step Equations and Inverse Operations

Add and subtract like terms as a step to solve equations.

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One-Step Equations Transformed by Multiplication-Division

Solving Equations with Multiplication and Division 

License: CC BY-NC 3.0

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.

Solving Equations 

1. 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.

2. 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.

3. Solve .

To cancel the 5, we divide both sides by 5.

4. 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....

Examples 

Example 1

is equivalent to , so to cancel out that , we multiply by the reciprocal, .

Example 2

.

Divide both sides by 7.

Review 

For 1-5, solve the following equations for .

For 6-10, solve the following equations for the unknown variable.

Review (Answers)

To view the Review answers, open this PDF file and look for section 3.2. 

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