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Solving Equations and Inequalities with Technology

Use technology to solve equations and inequalities. Understand the relationship between functions graphically and algebraically. Determine solutions for quadratic and linear equations as well as inequalities.

johnavon-gavin
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Solving Equations and Inequalities with Technology

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  1. Solving Equations and Inequalities with Technology

  2. Solve: NOW, consider TWOfunctions y = Left Side and y = Right Side y = 5x – 3 and y =2

  3. x = 1

  4. x = 1

  5. NOTE Blue GraphABOVE Red Graph The y-value of the function corresponding to the Left Sideis greater thanthe y-value of the function corresponding to the Right Side The function corresponding to the Left Sideis abovethe function corresponding to the Right Side x < 1

  6. Solve: x = -2 x = 3

  7. Now consider . . . x = -2 x = 3 x < -2 OR x > 3 For what values of x is the quadratic ABOVE the linear?

  8. Solve:

  9. Consider the inequality: RedBelowBlue …which is the solution to: A “small” gap for -1 < x < - 0.8 x = - 0.8 x ≥ - 0.8 x ≤ -1 or

  10. Using technology, the intersection points will be . . . All of the early examples COULD be solved algebraically. Now consider (1.73, 0.99) x = - 1.06 OR x = 1.73 (-1.06, -0.87)

  11. Consider the solution to the corresponding inequality. What is the solution for: x2 > sin(x)? (1.73, 0.99) - 1.06 < x < 1.73 (-1.06, -0.87)

  12. Now consider the solution to: (3.54, 4.21) (-0.30, 0.88) (-2.95, 0.30) x = 3.54 x = -2.95 x = -0.30 OR OR

  13. And the inequality: (3.54, 4.21) (-0.30, 0.88) (-2.95, 0.30) x ≥ 3.54 -2.95 ≤ x ≤ - 0.30

  14. and there’s much, much more . . .

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