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Absolute Value Equations

L
Lori Rapp

The document discusses solving absolute value equations. It explains that absolute value is the distance a number is from 0, and provides examples. It then states that when solving absolute value equations, two separate equations must be created to account for the number inside the absolute value being positive or negative. Steps are provided for solving sample absolute value equations.

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Solving Absolute Value Equations
Absolute Value Absolute Value is the distance a number is from 0.
Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3
Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3 When solving an absolute value equation, you need to account for the number inside the absolute value could be positive OR negative.
Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3 When solving an absolute value equation, you need to account for the number inside the absolute value could be positive OR negative. So 2 equation must be created to solve absolute value equations.
Solve for x: x−5 =8
Solve for x: x−5 =8 Split into 2 equations.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. Solve each equation.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 Solve each equation.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 Solve each x = 13 equation.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 Check both solutions.
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? Check both 13 − 5 = 8 solutions. ? 8 =8 8=8
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? ? Check both −3 − 5 = 8 13 − 5 = 8 solutions. ? ? −8 = 8 8 =8 8=8 8=8
Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? ? Check both −3 − 5 = 8 13 − 5 = 8 solutions. ? ? Write answer. −8 = 8 8 =8 8=8 8=8 {−3,13}
Solve for x: 2x + 1 = 7
Solve for x: 2x + 1 = 7 Split into 2 equations.
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 equations.
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 equations. Solve each equation.
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each equation.
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation.
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation. 2 2
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation. 2 2 x=3
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2 2 x=3
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 x=3
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 2 2 x=3
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 2 2 x=3 x = −4
Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 Check both 2 2 solutions on x=3 next page. x = −4
Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 solutions. Write answer.
Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. 2 ( 3) + 1 = 7 Write answer. ? 7 =7 7=7
Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. ? 2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7 Write answer. ? ? 7 =7 −7 = 7 7=7 7=7
Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. ? 2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7 Write answer. ? ? 7 =7 −7 = 7 7=7 {−4, 3} 7=7
Solve for x: x − 5 = 2x
Solve for x: x − 5 = 2x Split into 2 equations.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x equations.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x equations. Solve each equation.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. Solve each equation.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. Solve each −5 = x equation.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each −5 = x equation.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation.
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5 3 3
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5 3 3 5 x= 3
Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 Check both 3x = 5 solutions on next page. 3 3 5 x= 3
Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 solutions. Only 1 solution works. So the answer is
Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. −5 − 5 = 2 ( −5 ) ? Only 1 −10 = − 10 solution 10 ≠ −10 works. So the answer is
Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. 5 ?  5 −5 − 5 = 2 ( −5 ) − 5 = 2  Only 1 3  3 ? −10 = − 10 solution −10 ? 10 = 10 ≠ −10 works. So the 3 3 answer is 10 10 = 3 3
Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. 5 ?  5 −5 − 5 = 2 ( −5 ) − 5 = 2  Only 1 3  3 ? −10 = − 10 solution −10 ? 10 = 10 ≠ −10 works. So the 3 3 answer is 10 10 = 5  3 3   3
Solve for x: 3x + 7 = x
Solve for x: 3x + 7 = x Split into 2 equations.
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x equations.
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x equations. Solve each equation.
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. Solve each equation.
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation.
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 2x = −7 2 2 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 2 2 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 4 4 −7 x= 2
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 4 4 −7 −7 x= x= 2 4
Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 Check both 4x = −7 2x = −7 solutions on 2 2 next page. 4 4 −7 −7 x= x= 2 4
Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4 solutions. Neither solution works so the answer is
Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  2 2 Neither solution −7 ? −7 = works so the 2 2 answer is 7 −7 ≠ 2 2
Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  −7  ? −7  2 Neither 3  + 7 = 2  4 4 solution −7 ? −7 7 ? −7 = works so the = 2 2 answer is 4 4 7 −7 7 −7 ≠ ≠ 2 2 4 4
Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  −7  ? −7  2 Neither 3  + 7 = 2  4 4 solution −7 ? −7 7 ? −7 = works so the = 2 2 answer is 4 4 7 −7 7 −7 ≠ ≠ 2 2 no solution 4 4

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Absolute Value Equations

  • 2. Absolute Value Absolute Value is the distance a number is from 0.
  • 3. Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3
  • 4. Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3 When solving an absolute value equation, you need to account for the number inside the absolute value could be positive OR negative.
  • 5. Absolute Value Absolute Value is the distance a number is from 0. |3| = 3 and |-3| = 3 When solving an absolute value equation, you need to account for the number inside the absolute value could be positive OR negative. So 2 equation must be created to solve absolute value equations.
  • 6. Solve for x: x−5 =8
  • 7. Solve for x: x−5 =8 Split into 2 equations.
  • 8. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations.
  • 9. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. Solve each equation.
  • 10. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 Solve each equation.
  • 11. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 Solve each x = 13 equation.
  • 12. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation.
  • 13. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3
  • 14. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 Check both solutions.
  • 15. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? Check both 13 − 5 = 8 solutions. ? 8 =8 8=8
  • 16. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? ? Check both −3 − 5 = 8 13 − 5 = 8 solutions. ? ? −8 = 8 8 =8 8=8 8=8
  • 17. Solve for x: x−5 =8 x−5=8 Split into 2 x − 5 = −8 equations. +5 +5 +5 +5 Solve each x = 13 equation. x = −3 ? ? Check both −3 − 5 = 8 13 − 5 = 8 solutions. ? ? Write answer. −8 = 8 8 =8 8=8 8=8 {−3,13}
  • 18. Solve for x: 2x + 1 = 7
  • 19. Solve for x: 2x + 1 = 7 Split into 2 equations.
  • 20. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 equations.
  • 21. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 equations. Solve each equation.
  • 22. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each equation.
  • 23. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation.
  • 24. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation. 2 2
  • 25. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. Solve each 2x = 6 equation. 2 2 x=3
  • 26. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2 2 x=3
  • 27. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 x=3
  • 28. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 2 2 x=3
  • 29. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 2 2 x=3 x = −4
  • 30. Solve for x: 2x + 1 = 7 2x + 1 = 7 Split into 2 2x + 1 = −7 −1 −1 equations. −1 −1 Solve each 2x = 6 equation. 2x = −8 2 2 Check both 2 2 solutions on x=3 next page. x = −4
  • 31. Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 solutions. Write answer.
  • 32. Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. 2 ( 3) + 1 = 7 Write answer. ? 7 =7 7=7
  • 33. Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. ? 2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7 Write answer. ? ? 7 =7 −7 = 7 7=7 7=7
  • 34. Solve for x continued... 2x + 1 = 7 x=3 Check both x = −4 ? solutions. ? 2 ( 3) + 1 = 7 2 ( −4 ) + 1 = 7 Write answer. ? ? 7 =7 −7 = 7 7=7 {−4, 3} 7=7
  • 35. Solve for x: x − 5 = 2x
  • 36. Solve for x: x − 5 = 2x Split into 2 equations.
  • 37. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x equations.
  • 38. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x equations. Solve each equation.
  • 39. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. Solve each equation.
  • 40. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. Solve each −5 = x equation.
  • 41. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each −5 = x equation.
  • 42. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation.
  • 43. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5
  • 44. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5
  • 45. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5 3 3
  • 46. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 3x = 5 3 3 5 x= 3
  • 47. Solve for x: x − 5 = 2x x − 5 = 2x Split into 2 x − 5 = −2x −x −x equations. +2x +2x Solve each 3x − 5 = 0 −5 = x equation. +5 +5 Check both 3x = 5 solutions on next page. 3 3 5 x= 3
  • 48. Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 solutions. Only 1 solution works. So the answer is
  • 49. Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. −5 − 5 = 2 ( −5 ) ? Only 1 −10 = − 10 solution 10 ≠ −10 works. So the answer is
  • 50. Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. 5 ?  5 −5 − 5 = 2 ( −5 ) − 5 = 2  Only 1 3  3 ? −10 = − 10 solution −10 ? 10 = 10 ≠ −10 works. So the 3 3 answer is 10 10 = 3 3
  • 51. Solve for x continued... x − 5 = 2x 5 x= −5 = x Check both 3 ? solutions. 5 ?  5 −5 − 5 = 2 ( −5 ) − 5 = 2  Only 1 3  3 ? −10 = − 10 solution −10 ? 10 = 10 ≠ −10 works. So the 3 3 answer is 10 10 = 5  3 3   3
  • 52. Solve for x: 3x + 7 = x
  • 53. Solve for x: 3x + 7 = x Split into 2 equations.
  • 54. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x equations.
  • 55. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x equations. Solve each equation.
  • 56. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. Solve each equation.
  • 57. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation.
  • 58. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7
  • 59. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7
  • 60. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2
  • 61. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2 −7 x= 2
  • 62. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each equation. −7 −7 2x = −7 2 2 −7 x= 2
  • 63. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 2x = −7 2 2 −7 x= 2
  • 64. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 2 2 −7 x= 2
  • 65. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 −7 x= 2
  • 66. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 4 4 −7 x= 2
  • 67. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 2x = −7 4x = −7 2 2 4 4 −7 −7 x= x= 2 4
  • 68. Solve for x: 3x + 7 = x 3x + 7 = x Split into 2 3x + 7 = −x −x −x equations. +x +x 2x + 7 = 0 Solve each 4x + 7 = 0 equation. −7 −7 −7 −7 Check both 4x = −7 2x = −7 solutions on 2 2 next page. 4 4 −7 −7 x= x= 2 4
  • 69. Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4 solutions. Neither solution works so the answer is
  • 70. Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  2 2 Neither solution −7 ? −7 = works so the 2 2 answer is 7 −7 ≠ 2 2
  • 71. Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  −7  ? −7  2 Neither 3  + 7 = 2  4 4 solution −7 ? −7 7 ? −7 = works so the = 2 2 answer is 4 4 7 −7 7 −7 ≠ ≠ 2 2 4 4
  • 72. Solve for x continued... −7 3x + 7 = x x= −7 x= 2 Check both 4  −7  ? −7 solutions. 3  + 7 =  −7  ? −7  2 Neither 3  + 7 = 2  4 4 solution −7 ? −7 7 ? −7 = works so the = 2 2 answer is 4 4 7 −7 7 −7 ≠ ≠ 2 2 no solution 4 4

Editor's Notes