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# Inequalities

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solve & graph inequalities

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### Inequalities

1. 1. Agenda Monday, Nov. 23 Homework 8 p. 136 # 12 - 20 p. 142 # 10 - 14, 39, 77, 79 p. 149 # 13 - 20, 29, 30 Don't panic, we will have some time in Flex to get started. Daily Scribe? Monday _____________ Tuesday ____________ Tutors? need papers today Chapter Three - Inequalities: graphs & solutions
2. 2. ADVISORY You must be at least 35 inches tall in order to ride Pirate Lagoon. Express this statement using algebra The Management Let x represent the height. x ≥ 35 36&quot; 35&quot; 34&quot; Which of the triplets can ride?
3. 3. Which graph represents the inequality x ≥ 35 x ≥ 35
4. 4. Match the inequality to the graph x > 35 x < 35 x ≤ 35 x ≥ 35 x ≥ 35 x ≤ 35 x > 35 x < 35
5. 5. x < 45 x ≥ 25 x ≤ -5 x > -2 Graph these inequalities on the number line
6. 6. x < 45 x ≥ 25 x ≤ -5 x > -2 Solution
7. 7. Identify the values which make the inequality true -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -5 -4 -3 -2 -1 0 1 2 3 4 5 2x + 1 ≤ 5 x + 5 > 11 } { {7,8,9,10} {-5,-4,-3,-2,-1,0,1,2} } {
8. 8. Solve these inequalities 3x - 4 > 14 x + 4 ≤ 3 5 Solve as inequality the same way you would solve a linear equation. Instead of &quot;=&quot; you have &quot;>, <, ≥ or ≤&quot;. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x 5 + x 5 ≤ -1 x ≤ -5 4 - 4 ≤ 3 - 4 3x - 4 + 4 > 14 + 4 3x > 18 3x > 18 3 3 x > 6
9. 9. -5 -4 < TRUE When you multiply or divide an inequality by a negative number the direction of the inequality must be reversed. Multiply both sides by -1 > 5 4 > TRUE FALSE Multiplying or dividing by a negative number -5 -4
10. 10. 4x + 2 > 10 - 4x + 2 > 10 Solve these inequalities x > 2 x < 2 x < -10 x > -10 x < -2 x > -2 x < 10 x > 10 3 - > 8 x 2 3 + > 8 x 2 x > 2 x > 10 3 - - 3 > 8 - 3 x 2 x 2 - > 5 x 2 (-2) < (5)(-2) - x < -10 - 4x + 2 - 2 > 10 - 2 - 4x > 8 8 4 - x -4 -4 < x < -2
11. 11. 4x + 2 > 10 - 4x + 2 > 10 3 - > 8 x 2 3 + > 8 x 2
12. 12. T he value the circle lies on is included in the solution set. Closed circle Open circle T he value the circle lies on is not included in the solution set. Open or closed? back to page 3
13. 13. Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. draw and measure the lengths of three triangles Compare the sum of the measures of the small and medium sides to the measure of the large side for each triangle you created. Describe what you notice. sm + med large medium small
14. 14. Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. draw and measure three lengths that cannot make a triangle Compare the sum of the measures of the small and medium sides to the measure of the large side for each non-triangle you created. Describe what you notice. sm + med large medium small
15. 15. Compare the sum of the measures of the small and medium sides to the measure of the large side for each triangle you created. Describe what you notice. Compare the sum of the measures of the small and medium sides to the measure of the large side for each non-triangle you created. Describe what you notice. Make a conjecture . Based on your observations, write a conjecture about the relationship between the sum of the measures of the small and medium sides of a triangle and the measure of the large side of the triangle. Provide a reason for your conjecture.
16. 18. Attachments