1 / 21

Understanding and Solving Equations with Variables on Both Sides

This lesson focuses on solving equations involving variables on both sides and those with grouping symbols. Students will learn to efficiently isolate variables using inverse operations and simplification techniques. Key concepts include combining like terms, applying distribution, and understanding special cases such as no solutions and infinite solutions. Through guided practice, students will solve various equations, including examples with step-by-step solutions. Prepare for your upcoming quiz by reviewing these essential skills!

melva
Télécharger la présentation

Understanding and Solving Equations with Variables on Both Sides

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. Bell Ringer Solve the following 2 equations

  2. Solving Equations: variables on BOTH sides The student will be able to: 1. solve equations with variables on both sides. 2. solve equations containing grouping symbols.

  3. 1) Solve. 3x + 2 = 4x - 1 You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

  4. Rules to remember • Simplify the left and the right separately • Use combining like terms and distribution • Solve by using inverse operations. • If you are moving anything over the equal sign, use inverse operations. If you are simplifying the separate sides, DO NOT use inverses

  5. 1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x 3(3) + 2 = 4(3) - 1 9 + 2 = 12 - 1 • Draw “the river” • Subtract 3x from both sides • Simplify • Add 1 to both sides • Simplify • Check your answer

  6. 2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11 y = 1 8(1) - 9 = -3(1) + 2 • Draw “the river” • Add 3y to both sides • Simplify • Add 9 to both sides • Simplify • Divide both sides by 11 • Simplify • Check your answer

  7. Answer Now What is the value of x if 3 - 4x = 18 + x? • -3 • 3

  8. 3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) • Draw “the river” • – Notice the variables are on the same side! • Combine like terms • Divide both sides by 4 • Simplify • Check your answer

  9. Let’s Throw in some Combining Like Terms!!!

  10. That’s All for Today!!! • Please do your DLIQ!!!

  11. Bell Ringer

  12. Homework Review

  13. YOU HAVE A QUIZ ON FRIDAY!!!!! • This quiz will cover the following: • 1 step Equations • 2 step easy equations • 2 step 2 “floor” equations • Multistep equations • Multistep equations with variables on both sides

  14. -7x + 21 = -7 - 21 - 21 -7x = -28 -7 -7 x = 4 -7(4 - 3) = -7 -7(1) = -7 • Draw “the river” • Distribute • Subtract 21 from both sides • Simplify • Divide both sides by -7 • Simplify • Check your answer 4) Solve -7(x - 3) = -7

  15. Answer Now What is the value of x if 3(x + 4) = 2(x - 1)? • -14 • -13 • 13 • 14

  16. 5) Solve • Draw “the river” • Clear the fraction – multiply each term by the LCD • Simplify • Add 2x to both sides • Simplify • Add 6 to both sides • Simplify • Divide both sides by 6 • Simplify • Check your answer 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6 or 1.5 = x

  17. Special Case #1 6) 2x + 5 = 2x - 3 -2x -2x 5 = -3 This is never true! No solutions • Draw “the river” • Subtract 2x from both sides • Simplify

  18. Special Case #2 7) 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinite solutions or identity • Draw “the river” • Distribute • Combine like terms • Subtract 3x from both sides • Simplify

  19. Answer Now What is the value of x if -3 + 12x = 12x - 3? • 0 • 4 • No solutions • Infinite solutions

  20. Answer Now Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2? • -8 • -2 • 2 • 8

More Related