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Solve two-step equations Solve equations with variables on both sides

Objectives The student will be able to:. Solve two-step equations Solve equations with variables on both sides Solve equations containing grouping symbols. Adapted from original designed by Skip Tyler, Varina High School. Solve: 8x + 5 = 61. Step 1. Step 2.

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Solve two-step equations Solve equations with variables on both sides

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  1. ObjectivesThe student will be able to: Solve two-step equations Solve equations with variables on both sides Solve equations containing grouping symbols. Adapted from original designed by Skip Tyler, Varina High School

  2. Solve: 8x + 5 = 61 Step 1 Step 2 Completely UNDO those steps Working in reverse order using inverse operations! Examine the problem Figure out the order that you would DO to solve if you knew the value of the variable. Use PEMDAS! + - ÷ •

  3. Solve: 8x + 5 = 61 – 5 – 5 8x = 56 x = 7 8(7) + 5 = 61 56 + 5 = 61 • Draw “the river” • Subtract 5 from both sides • Simplify • Divide both sides by 8 • Simplify • Check your answer 8 8

  4. Answer Now Find the value of z if 7z + 5 = 40 • 245 • 5 • 9 • 315

  5. Solve: + 9 + 9 = 40 a = −160 40 − 9 = 31 • Draw “the river” • Add 9 to both sides • Simplify • Multiply both sides by -4 • Simplify • Check your answer −4   −4

  6. Solve: • Draw “the river” • Subtract 8 from both sides • Simplify • Multiply both sides by 4 • Simplify • Check your answer − 8 − 8 = − 20 y = −80 −20 + 8 = −12 4   4

  7. Answer Now Find the value of z if • 30 • 4 • 100 • 1.2

  8. Solve: • Draw “the river” • Multiply both sides by 3 • Simplify • Add 8 to both sides • Simplify • Check your answer = (4)3 m – 8 = 12 + 8 = + 8 m= 20 12/3 = 4

  9. Answer Now Find the value of z if • 186 • 51 • 39 • 174

  10. 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.

  11. 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

  12. 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

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

  14. 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

  15. – 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 Solve: – 7(x – 3) = – 7

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

  17. 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

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

  19. Special Case #23(x + 1) – 5 = 3x – 2 3x + 3 – 5 = 3x – 2 3x – 2 = 3x – 2 – 3x – 3x – 2 = – 2 • Draw “the river” • Distribute • Combine like terms • Subtract 3x from both sides • Simplify This is always true! Infinite solutions or identity

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

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

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