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You are reading an older version of this FlexBook® textbook: CK-12 Algebra I Concepts Go to the latest version.

3.2: One-Step Equations Transformed by Multiplication-Division

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Practice One-Step Equations Transformed by Multiplication/Division
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What if you had an algebraic equation involving multiplication or division like 5x=3? 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)


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 8×$1.50=$12.00. You solved this problem by multiplying. Here’s how to do the same thing algebraically, using x to stand for the cost in dollars of the whole pizza.

Example A

Solve 18x=1.5.

Our x is being multiplied by one-eighth. To cancel that out and get x by itself, we have to multiply by the reciprocal, 8. Don’t forget to multiply both sides of the equation.


Example B

Solve 0.25x=5.25.

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 x. 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 5x=3.25.

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


Example D

Solve 1.375x=1.2.

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


  • 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


a) 9x5=5.

b) 7x=511.


a) 9x5 is equivalent to 95x, so to cancel out that 95, we multiply by the reciprocal, 59.


b) Divide both sides by 7.



For 1-5, solve the following equations for x.

  1. 7x=21
  2. 4x=1
  3. 5x12=23
  4. 0.01x=11
  5. 2x9=103

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

  1. 21s=3
  2. 7a=5
  3. 7f11=711
  4. 6r=38
  5. 9b16=38

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Difficulty Level:

At Grade


Date Created:

Aug 13, 2012

Last Modified:

Oct 08, 2015
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