4-5: Compound Inequalities Essential Question: Explain the difference between compound inequalities with “and” and those with “or”.

4-5: Compound Inequalities Two inequalities that are joined by the word and or the word or form a compound inequality. You can write the compound inequality x > -5 and x < 7 as -5 < x < 7 An “and” inequality has two “ends” when graphed

4-5: Compound Inequalities Example 1: Writing a Compound Inequality All real numbers that are at least -2 and at most 4 n > -2 and n < 4 -2 < n < 4 Today’s high temperature will be above 32º F, but not as high as 40º F 32 < t < 40

4-5: Compound Inequalities Your Turn Write a compound inequality that represents each situation. Then graph your solution. All real numbers greater than -2 but less than 9 -2 < x < 9 The books were priced between $3.50 and $6.00, inclusive 3.50 < x < 6.00

4-5: Compound Inequalities A solution to an “and” inequality is any number that makes both inequalities true. One way you can solve a compound inequality is by writing two equations. Example 2: Solving a Compound Inequality containing “And” -4 < r – 5 < -1 -4 < r – 5 And r – 5 < -1 +5 +5 + 5 +5 1 < r r < 4 1 < r < 4

4-5: Compound Inequalities Your Turn Solve each inequality. Graph your solution. -6 < 3x < 15 -2 < x < 5 -3 < 2x – 1 < 7 -1 < x < 4

4-5: Compound Inequalities A solution of a compound inequality containing “or” is any number that makes either inequality true. Example 4: Writing a Compound Inequality All real numbers that are at most 3 or greater than 7 n < 3 or n > 7 An “or” inequality has two “oars” (like with a boat) when graphed

4-5: Compound Inequalities Your Turn Write a compound inequality that represents each situation. Then graph your solution. All real numbers that are at most -5 or at least 3 n < -5 or n > 3

4-5: Compound Inequalities To solve “or” inequalities, simply solve the two inequalities separately. Example 5: Solving a Compound Inequality containing “Or” 4v + 3 < -5 Or -2v + 7 < 1 - 3 -3 - 7 -7 4v < -8 -2v < -6 ÷4 ÷4 ÷-2 ÷-2 v < -2 Or v > 3

4-5: Compound Inequalities Assignment Worksheet 4-5 1 – 17 and 23 – 37 Odd Problems