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Solving For Variables

Solving For Variables. By Amy Beyer. Getting the Variable alone. To solve for a variable you must get the variable alone. Do the opposite of what is being done to the variable (if a number is being added to it, subtract that number)

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Solving For Variables

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  1. Solving For Variables By Amy Beyer

  2. Getting the Variable alone • To solve for a variable you must get the variable alone. • Do the opposite of what is being done to the variable (if a number is being added to it, subtract that number) • What you do to one side you must do the same thing to the other side to keep both sides the same value.

  3. Reverse of Order of Operation • When solving for a variable do the reverse of the Order of Operations: • First add or subtract • Second multiply or divide

  4. Checking Your Answer • Once you have solved for the variable you can check to make sure the number you got is right. • To do this take the answer and substitute it into the problem for the variable. • If the problem is true with the substitution, you have the right answer.

  5. Addition: X + 5 = 10 X + 5 – 5 = 10 – 5 X = 5 Since 5 is being added to the variable, subtract 5 from both sides to get the variable alone. This will cancel out the 5 being added Once you have subtracted 5 from both sides, you’ll have the variable alone and your answer. Example of Addition

  6. Subtraction: X – 4 = 2 X – 4 + 4 = 2 + 4 X = 6 Since 4 is being subtracted from the variable, add 4 to both sides to get rid of it. This cancels out the 4 being subtracted. Now, you’ll have the variable alone and what it is equal to Example of Subtraction

  7. Multiplication 3x = 9 3x/3 = 9/3 x = 3 Since the variable is being multiplied by 3, to cancel that out both sides need to have 3 divided into them. This gets the variable alone and shows what it is equal to. Example of Multiplication

  8. Division x/5 = 3 x/5 × 5 = 5 × 3 x = 15 In this example, the variable is being divided by 5. So to get rid of the division both sides must be multiplied by 5. This gets the variable alone and gives the value for x. Example of Division

  9. Example: 3x + 5 = 20 3x + 5 – 5 = 20 – 5 3x = 15 3x/3 = 15/3 x = 5 First subtract 5 from both sides Next you divide both sides by 3 Last you have what x is equal to Example of Addition and Multiplication in the Same Problem

  10. Addition and Subtraction in the Same Problem • If a problem has both addition and subtraction combine the two numbers together and then get the variable alone. • Example: 4 + x – 2 = 6 4 – 2 + x = 6 2 + x = 6 2 – 2 + x = 6 – 2 x = 4

  11. Multiplication and Division in the Same Problem • If a problem has both multiplication and division get rid of the division first by multiplying and then get rid of the number that is multiplying the variable. • Example: 3x/9 = 6 3x/9 × 9 = 6 × 9 3x = 54 3x/3 = 54/3 X = 18

  12. Additional Information • Paul's Online Math Tutorials and Notes • This site offers explanation of how to solve for a variable and examples to look at if you are stuck on a problem. • Solving an Equation • This site has examples of addition and subtraction with directions of how to do them and then an interactive section where students can practice problems. The page starts with addition and subtraction, to move onto multiplication and division by clicking on next lesson at the tope on the screen. Then, if you push next lesson it will continue with putting addition, subtraction, multiplication, and division.

  13. Additional Information • Instructions • Here are additional instructions to help explain how to solve for variables • Practice Worksheet • This is a practice worksheet covering addition, subtraction, multiplication, and division all put together in solving for variables. • Practice Worksheet Answers

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