Solving Compound Inequalities Continued…

Example 1 Translate the verbal phrase into an inequality. Then graph the inequality. All real numbers that are greater than –2 and less than 3 1. Inequality: All real numbers that are less than 0 or greater than or equal to 2 3. Inequality: Warm-up 2. Graph: 4. Graph:

Example 1 Translate the verbal phrase into an inequality. Then graph the inequality. All real numbers that are greater than –2 and less than 3 1. Inequality: All real numbers that are less than 0 or greater than or equal to 2 3. Inequality: –2 < x < 3 x < 0 or x  2 Warm-up 2. Graph: 4. Graph:

Compound Inequality – two separate inequalities join by and or or. OR Union of the graphs of the inequalities Must answer either of the inequalities AND Intersection of the graphs of the inequalities. Must answer both inequalities. Let’s Review…

Example 2 CAMERA CARS A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4  h  18.

Solve: 2x < -6 and 3x ≥ 12 Solve each inequality Graph each solution Where do they intersect? They do not! No Solution !! o o 471 o ● 471 o ●

Solve: 3x+2 < 2 or 1-x ≥ o ● Unite the two sets o ●

Graph x > -1 or x < 3 The entire number line is shaded!! What is the solution??? {all real numbers} 03

Guided Practice 6 – x ≤ 4 and 4x + 9 < -3 Solve the inequality, if possible. Graph your solution. n + 19 ≥ 10 or -5n + 3 > 33

Solve and graph

Using logic with inequalities