1 / 10

Solving Equations and Finding Solutions

Learn how to solve equations and find the value of the variable that makes the equation true. Use inverse operations and properties of addition and subtraction to isolate the variable. Practice examples and quizzes included.

lark
Download Presentation

Solving Equations and Finding Solutions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

  2. ? ? x + 8 = 15 5 + 8 = 15 ? 13= 15 Additional Example 1: Determining Whether a Number is a Solution of an Equation Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 5 for x.  So 5 is not solution.

  3. ? ? x + 8 = 15 7 + 8 = 15 ? 15= 15 Additional Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 7 for x.  So 7 is a solution.

  4. ? ? x + 8 = 15 23 + 8 = 15 ? 31= 15 Additional Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 23 for x.  So 23 is not a solution.

  5. 4 WORDS To Remember • Isolate-Inverse-Both Sides • Isolate the variable • Using inverse operations • Perform operations on both sides of the equation

  6. Inverse (Opposite) Operations • Addition – Subtraction • Subtraction – Addition • Multiplication – Division • Division - Multiplication

  7. ? 10 + 8 = 18 ? 18 = 18 Additional Example 2A: Solving Equations Using Addition and Subtraction Properties Solve. 10 + n = 18 10 + n = 18 Since 10 is added to n, subtract 10 from both sides to undo the addition. –10 –10 0 + n = 8 n = 8 Identity Property of Addition: 0 + n = n. Check 10 + n = 18 To check your solution, substitute 8 for n in the original equation. 

  8. ? 17 – 8 = 9 ? 9 = 9 Additional Example 2B: Solving Equations Using Addition and Subtraction Properties Solve. p – 8 = 9 p – 8 = 9 Since 8 is subtracted from p, add 8 to both sides to undo the subtraction. + 8 + 8 p + 0= 17 Identity Property of Addition: p + 0 = p. p = 17 Check p – 8 = 9 To check your solution, substitute 17 for p in the original equation. 

  9. ? 22 = 33 – 11 ? 22 = 22 Additional Example 2C: Solving Equations Using Addition and Subtraction Properties Solve. 22 = y – 11 22 = y – 11 + 11 + 11 Since 11 is subtracted from y, add 11 to both sides to undo the subtraction. 33 = y + 0 33 = y Identity Property of Addition: y + 0 = y. Check 22 = y – 11 To check your solution, substitute 33 for y in the original equation. 

  10. Lesson Quiz Determine which value of x is a solution of each equation. 1.x + 9 = 17; x = 6, 8, or 26 2.x – 3 = 18; x = 15, 18, or 21 Solve. 3.a + 4 = 22 4.n – 6= 39 5. The price of your favorite cereal is now $4.25. In prior weeks the price was $3.69. Write and solve an equation to find n, the increase in the price of the cereal. 8 21 a = 18 n = 45 3.69 + n = 4.25;$0.56

More Related