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Warm Up

Warm Up. Solve the equation. answers. x = 7 and x = -3 x = 3 and x = -2 x = 5 and x = 1 x = -2 ½ and x = -6 ½ x = 1 and x = -2. 3.5 Solving and Graphing Inequalities. What is an inequality? What are the inequality signs?.

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Warm Up

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  1. Warm Up Solve the equation.

  2. answers • x = 7 and x = -3 • x = 3 and x = -2 • x = 5 and x = 1 • x = -2 ½ and x = -6 ½ • x = 1 and x = -2

  3. 3.5 Solving and Graphing Inequalities

  4. What is an inequality? What are the inequality signs? An inequality is a statement that shows how two expressions compare, using greater than or less than symbols.

  5. Write each pair of numbers, write an inequality symbol to compare them, and perform the indicated steps. Add four to each side. Compare the answers. Subtract five from each side. Compare the answers. 5 8 5 < 8 9 < 12 4 < 7 Exploration

  6. Write each pair of numbers, write an inequality symbol to compare them, and perform the indicated steps. Add ten to each side. Compare the answers. Subtract seven from each side. Compare the answers. -3 -8 -3 > -8 7 > 2 0 > -5 Exploration

  7. What did you notice? • Summarize what you noticed about the inequality sign after performing the indicated operations. • Adding or subtracting the same number to both sides of the inequality does not change the inequality sign.

  8. Write each pair of numbers, write an inequality symbol to compare them, and perform the indicated steps. Multiply by four on each side. Compare the answers. Divide by two on each side. Compare the answers. 4 -12 4 > -12 16 > -48 8 > -24 Exploration

  9. Write each pair of numbers, write an inequality symbol to compare them, and perform the indicated steps. Multiply by negative two on each side. Compare the answers. Divide by negative four on each side. Compare the answers. -6 10 -6 < 10 12 > -20 -3 < 5 Exploration

  10. What did you notice? • Summarize what you noticed about the inequality sign after performing the indicated operation. • Multiplying or dividing by a positive number on both sides does not affect the inequality sign. • Multiplying or dividing by a negative number on both sides changes the direction of the inequality sign.

  11. Steps for Solving an Inequality Distribute Combine like terms Move the variable to one side Undo addition or subtraction Undo multiplication or division (if mult. or div. by a neg. change sign)

  12. Steps for Graphing an Inequality Draw a number line including the number in the solution. Draw a circle around the value in the solution. Fill in the circle if the value is a part of the solution, leave it open if it is not part of the solution. Draw an arrow in the direction of the values in the solution.

  13. 4 5 6 7 8 9 x > 6 -5 -4 -3 -2 -1 0 -3 > x x < -3 Examples Solve and graph each inequality. • x + 7 > 13 • -21 > x - 18

  14. -14 -12 -10 n -12 -14 -12 -10 Examples • Solve and graph each inequality.

  15. -9 -7 -5 -3 -1 0 0 2 4 6 8 Examples Solve and Graph 5) 2x + 1 > 13 6) 7 – 2t > 21 -7 - 7 - 1 -1 -2t > 14 2x > 12 -2 -2 2 2 X > 6 t < -7

  16. Try These: solve and graph 7. 3 – 3x + 2 > 5 – 2x 8. 4m – 4 < 2 + 4m 9. -3(x – 2) < 3 – (2x + 4) • Answers • 7. 0 > x 0 • 8. I.M.S • 9. 7 < x 7

  17. Summary/Reflection • How is solving an inequality alike and different from solving an equation? • How will you remember which direction to draw the arrow on the graph? • How will you remember whether to use an open or closed circle?

  18. Homework • Worksheet 3.5

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