1 / 15

Solving Linear Equations: Addition and Subtraction Techniques

This educational guide explores the process of solving linear equations through addition and subtraction techniques suitable for students learning basic algebra. It covers key objectives such as identifying operations, applying opposite operations, and isolating variables. Through step-by-step examples, learners will understand how to manipulate equations to isolate the variable, verify solutions, and eliminate complex signs. Emphasis is placed on balancing equations like a scale to ensure clarity in problem-solving.

vicky
Télécharger la présentation

Solving Linear Equations: Addition and Subtraction Techniques

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. OTCQ evaluate expression if x =2, a = 5 and k = 3. k(xa + ax) = ?

  2. AIM3-2 How do we solve equations by using addition and subtraction?NYAA 6

  3. New York StandardsA.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

  4. Objectives • SWBAT to identify operations and their opposites. • SWBAT to apply opposite operations in reverse PEMDAS order. • SWBAT to isolate a variable.

  5. r + 16 = -7 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

  6. 1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

  7. 1) Solve r + 16 = -7 • Draw “the river” to separate the equation into 2 sides • Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem - 16 -16 r = -23 -23 + 16 = -7

  8. 2) Solve x + 2 = -3Get the variable by itself. What is your first step? • Add 2 to both sides • Subtract 2 from both sides • Add 3 to both sides • Subtract 3 from both sides

  9. 2) Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 • Draw “the river” to separate the equation into 2 sides • Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  10. 3) Solve 8 = m - 3 • m = 5 • m = 11 • m = 24 • m = 8/3

  11. 3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 • Draw “the river” to separate the equation into 2 sides • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  12. When solving equations, we want to eliminate double signs. y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

  13. 4) Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 • Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  14. 5) Solve. -x - (-2) = 1 • Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • Subtract 2 from both sides • Simplify vertically • We haven’t gotten x by itself. If we read this aloud, it is “the opposite of x equals -1”. What would x be equal? • Check your answer -x + 2 = 1 - 2 - 2 -x = -1 x = 1 -(1) + 2 = 1

  15. Solve -y – (-3) = 7 • y = 10 • y = 4 • y = -10 • y = -4

More Related