Solving Compound Inequalities

Lesson 39 Compound and Absolute Value InequalitiesNCSCOS 1.01;4.01Daily ObjectivesTLW solve compound inequalities.TLW graph the solution sets of compound inequalities.TLW solve absolute value inequalities

1) Graph x < 4 and x 2342a) Graph x < 4b) Graph x 2342oc) Combine the graphs342od) Where do they intersect?342o2) Graph x < 2 or x 4342a) Graph x < 2b) Graph x 4342oc) Combine the graphs342o3423) Which inequalities describe the following graph?-2-1-3ooAnswer Nowy > -3 or y < -1y > -3 and y < -1y -3 or y -1y -3 and y -1When written this way, it is the same thing as 6 < m AND m < 8It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,it is easier to graph everything between 6 and 8!4) Graph the compound inequality 6 < m < 8786oo5) Which is equivalent to-3 < y < 5?y > -3 or y < 5y > -3 and y < 5y < -3 or y > 5y < -3 and y > 5

Answer Now6) Which is equivalent to x > -5 and x 1?-5 < x 1-5 > x 1-5 > x 1-5 < x 1

Answer Now7) 2x < -6 and 3x 12Solve each inequality for xGraph each inequalityCombine the graphsWhere do they intersect?They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!!

-30-6o471o471o-30-6o8) Graph 3 < 2m + 1 < 9Remember, when written like this, it is an AND problem!3 < 2m + 1 AND 2m + 1 < 9Solve each inequality.Graph the intersection of 2 < m and m < 3.05-59) Graph x < 2 or x 405-510) Graph x -1 or x 3The whole line is shaded!!

Example 5-3a

Then graph the solution set.Writeasand

Original inequality

Add 3 to each side.

Simplify.Case 1Case 2Answer: The solution set is

Example 5-3b

Then graph the solution set.

Answer:

Example 5-4a

Case 1Case 2Then graph the solution set.

Writeasor

Add 3 to each side.

Simplify.

Original inequality

Divide each side by 3.

Simplify.

Example 5-4a

Answer: The solution set is

Example 5-4b

Then graph the solution set.

Answer:

-5

0

5