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Solving Equations and Inequalities with Technology

Solving Equations and Inequalities with Technology. Solve:. NOW, consider TWO functions. y = Left Side and y = Right Side y = 5x – 3 and y = 2. x = 1. x = 1. NOTE. Blue Graph ABOVE Red Graph.

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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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