1. Graphing Linear Inequalities 6.1 & 6.2

2. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Check whether the given number is a solution of the Inequality. 2.4m > –23; –6 ANSWERyes ANSWERno 1. x 3 ≤ 7; 20 Warm-Up Add. 5) 6) ANSWERyes ANSWER –4 3. Is 4 a solution of the inequality 2a – 1.5 ≥ 6? 4. Solve the equation of + 8 = 7. f 4

3. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. What’s the Difference? 4x + 2 = 3y4x + 2 < 3y

4. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Steps to Solving Linear Inequalities Solve for the variable. ▫If you multiple or divide by a negative number, then you change the sign of the inequality   > changes to <  Example: -2x < 5 ▫Otherwise, solve as you normally would (if their was an equal sign).

5. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Graph the Linear Inequality Graph it on a number line. ▫  The number is not a solution (> or <) ▫   The number is a solution (≤ or ≥) x > -6.5 x ≤ 4 a.a. b.b.

6. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. x – 5 > – 3.5 x – 5 + 5 > – 3.5 + 5 x > 1.5 ANSWER The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for x in the original inequality. x – 5 > – 3.5. Graph your solution. Solve Write original inequality. Add 5 to each side. Simplify.

7. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE Solve the inequality. Graph your solution. x – 9 ≤ 3 x – 9 + 9 ≤ 3 + 9 x ≤ 12 Write original inequality. Add 9 to each side. Simplify. 4. x – 9 ≤ 3 SOLUTION ANSWER The solutions are all real numbers less than 12. Check by substituting a number less than 12 for x in the original inequality.

8. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE SOLUTION 5. p – 9.2 < – 5 p – 9.2 < – 5 p – 9.2 + 9.2 < – 5 + 9.2 x < 4.2 Write original inequality. Add 9.2 to each side. Simplify. ANSWER The solutions are all real numbers less than 4.2. Check by substituting a number less than 4.2 for x in the original inequality.

9. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE Write original inequality. Simplify. 6. – 1 ≥ m – 1 2 – 1 ≥ m – 1 2 – 1 + ≥ m + 1 2 1 2 1 2 ≥ m 1 2 – Add to each side. 1 2 ANSWER The solutions are all real numbers less than. Check by substituting a number less than for x in the original inequality. 1 2 – 1 2 –

10. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. EXAMPLE 4 Solve 9  x + 7. Graph your solution. > 9 ≥ x + 7 Write original inequality. 9 – 7 ≥ x + 7 – 7 Subtract 7 from each side. 2 ≥ x Simplify. ANSWER You can rewrite 2 ≥ x as x ≥ 2. The solutions are all real numbers less than or equal to 2.

11. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. EXAMPLE 1 x 4 < 5. Write original inequality. x 4 < 4 4 5 Multiply each side by 4. x < 20 Simplify. ANSWER The solutions are all real numbers less than 20. Check by substituting a number less than 20 in the original inequality.. Graph your solution. x 4 < 5 Solve

12. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Solve the inequality. Graph your solution. 1. > 8 x 3 x 3 > 8. Write original inequality. Multiply each side by 8. x > 24 Simplify. ANSWER The solutions are all real numbers are greater than 24. Check by substituting a number greater than 24 in the original inequality. SOLUTION x 3 > 8 3 3

13. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE 2. ≤ – 2 m 8 Write original inequality. Multiply each side by 8. Simplify. ANSWER The solutions are all real numbers less than are equal to – 16. Check by substituting a number less than – 16 in the original inequality. SOLUTION m 8 ≤ – 2 m < – 16 m 8 8 3 ≤ – 2

14. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE Write original inequality. Multiply each side by 2.5. Simplify. ANSWER The solutions are all real numbers less than are equal to – 10. Check by substituting a number greater than – 10 in the original inequality. SOLUTION y ≥ – 10 3. ≥ – 4 y 2.5 ≥ – 4 y 2.5 8 ≥ – 4 y 2.5

15. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. EXAMPLE 2 < 7.< 7. x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > – 42 Simplify. ANSWER The solutions are all real numbers greater than – 42. Check by substituting a number greater than – 42 in the original inequality. < 7. Graph your solution. x –6 Solve x –6 > –6 –6 7

16. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. EXAMPLE 2 CHECK Write original inequality. Substitute 0 for x. Solution checks x – 6 < 7 0 – 6 < 7 ? 0 < 7

17. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. EXAMPLE 3 –3x > 24. –3x–3x –3 < 24 –3 x < – 8 Write original inequality. Divide each side by –3. Reverse inequality symbol. Simplify. –3x > 24. Solve

18. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. Multiply each side by – 4. Simplify. ANSWER The solutions are all real numbers greater than are equal to – 48. Check by substituting a number greater than – 48 in the original inequality. SOLUTION x < – 48 4. > 12 x – 4 x > 12 – 4 12 < – 4 x – 4

19. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. Multiply each side by – 7. Simplify. SOLUTION m < – 11.2 5. < 1.6 m – 7 m < 1.6 – 7 1.6 < – 7 m – 7

20. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. ANSWER The solutions are all real numbers greater than are equal to 9. Check by substituting a number greater than 9 in the original inequality. SOLUTION 6. 5v ≥ 45 5v ≥ 45 5v5v 5 ≥ 45 5 v ≥ 9 Divide both the side by 5. Simplify.

21. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. GUIDED PRACTICE Write original inequality. ANSWER The solutions are all real numbers greater than are equal to – 4. Check by substituting a number greater than – 4 in the original inequality. SOLUTION 7. – 6n < 24 – 6n < 24 > – 6n– 6n 66 24 66 n > – 4 Divide both the side by  6. Simplify.

22. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Solve a two-step inequality EXAMPLE 1 3x – 7 < 8 Write original inequality. 3x < 15 Add 7 to each side. x < 5 Divide each side by 3. ANSWER The solutions are all real numbers less than 5. Check by substituting a number less than 5 in the original inequality. 3x – 7 < 8. Graph your solution. Solve

23. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Solve a two-step inequality EXAMPLE 1 CHECK Write original inequality. Solution checks. Substitute 0 for x. ? 3 (0) – 7 < 8 –7 < 8 3x –7 < 8

24. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Solve a multi-step inequality EXAMPLE 2 Write original inequality. –0.6 ( x – 5) < 15 – –0.6x + 3 < 15 – Distributive property Subtract 3 from each side. – x > –20 Divide each side by 0.6. Reverse inequality symbol. – Solve – 0.6(x – 5) < 15 – – 0.6x < 12 –

25. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. Add 5 to both side. Divide each side by 2. ANSWER The solutions are all real numbers less than equal to 14. Check by substituting a number less than 14. Solve the inequality. Graph your solution. 2x – 5 23 < – 2x – 5 23. 1. < – 2x 28 < – x 14 < –

26. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. Divide the equation by 6. Simplify. ANSWER The solutions are all real numbers less than or equal to 3.5. Check by substituting a number less than 3.5. Solve the inequality. Graph your solution. – 6y +5 –16. 2. < – y 3.5 > – – 6y +5 –16 < – –6–6 –16 –5 < – y

27. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Write original inequality. Distributive property. ANSWER The solutions are all real numbers greater than 20. Check by substituting a number greater than 20. Solve the inequality.graph your solution 3. –1 4 ( p –12) > –2 –1 4 ( p –12) > 12 – p + 12 > –8 – p > –8 – 12 p < 20

28. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Identify the number of solutions of an inequality Solve the inequality, if possible. Graph your solution. 5. 5(m + 5) < 5m + 17 SOLUTION Write original inequality. Distributive property 25 < 17 Subtract 5m from each side. ANSWER There are no solutions because 25 < 17 is false. 5(m + 5) < 5m + 17 5m + 25 < 5m + 17

29. 6.1 & 6.2 Students will be able to graph linear inequalities with one variable. Identify the number of solutions of an inequality Write original inequality. Distributive property Subtract 8s from each side. Solve the inequality,if possible. Graph your solution. 1 – 8s –4(2s –1). 6. < – 1 – 8s –4(2s –1) < – 1 – 8s 8s + 4 < – 1 4 < – ANSWER All real numbers are solutions because is true. 1 4 < – SOLUTION