Unit 2: inequalities Final Exam Review

Topics to cover Graphing Inequalities Solving Inequalities Word Problems Compound Inequalities

Graphing Inequalities In this unit, we learned how to graph inequalities on NUMBER LINES There are 2 things you must take care of: What type of circle to use (OPEN OR CLOSED) Which way to draw the arrow (LEFT OR RIGHT) Circle: Open: > OR < Closed: ≥ OR ≤ Arrow: Left: < OR ≤ Right: > OR ≥

Graphing Inequalities Example: x < 2 g ≥ -4 You Try! 1. m ≤ 5 2. w > 0 3. -7 > d (be careful)

Graphing Inequalities Going Backwards! Example: s ≤ -2 h > -2 You Try! 1. 2. 3.

Solving inequalities You solve inequalities very similar to solving EQUATIONS First, COMBINE LIKE TERMS, then solve for the variable. To finish the problem, GRAPH the inequality. BE CAREFUL! Whenever to multiply or divide by a NEGATIVE NUMBER, you must SWITCH the inequality Example: -2x + 5 ≥ 3 Subtract 5  -2x ≥ -2 Divide by -2 (SWITCH THE SIGN)  x ≤ 1

Solving inequalities You Try! 1. 3(x + 1) < 15 2. 4x + 18 ≥ 2 3. -4x – 5 < 15 4. 3x – (-2) > 5x – 12

Word Problems Inequality word problems use a lot of vocabulary. Here is a list of the words that go with each symbol: >  More Than Above Greater Than <  Less Than Below Fewer Than   ≥ At Least Minimum No Less Than ≤ At Most Maximum No More Than

Word Problems Example: The sum of five times a number and two times and number is at least fourteen. 5x + 2x ≥ 14 7x ≥ 14 x ≥ 2

Word Problems You Try! The product of a number and three is less than negative twelve Five less than a number is under eleven Negative six times a number is at most forty-eight

Compound inequalities Compound Inequalities occur when you have 2 different inequalities written TOGETHER and graphed on the SAME number line. Example: 𝒙<𝟐 𝒐𝒓 𝒙>𝟒 𝒙≥𝟏 𝒂𝒏𝒅 𝒙≤𝟔

Compound inequalities You Try! Graph the following compound inequalities 1. 𝒙<𝟒 𝑶𝑹 𝒙≥𝟖 2. 𝒙>𝟐 𝑨𝑵𝑫 𝒙<𝟔

Compound inequalities Solving Compound Inequalities SEPARATE the inequality into 2 different inequalities. REPEAT the term in the middle Example: -1 < x + 9 < 17 Separate  -1 < x + 9 and x + 9 < 17 Solve  -10 < x and x < 8

Compound inequalities You Try! 𝟏𝟐<𝟐𝒙+𝟐≤𝟐𝟎 𝟑𝒙−𝟏≤𝟓<𝟒𝒙+𝟏𝟑

ALL DONE