WARM UP Graph the line: Solve this equation: y = (2/3)x + 4 3x + 4 = 6x - 5

SEPTEMBER 24 TH SOLVING AND GRAPHING INEQUALITIES

GRAPHING INEQUALITIES Inequalities represent a set of numbers When you see sign you need to have an open dot on your graph When you see ≤ or a ≥ sign in your solution you will need to have a closed dot on your graph

GRAPHING INEQUALITIES Examples: 1. x < 5 2. x ≥ 11 A solution to an inequality is any number that makes the inequality true.

SOLUTIONS OF INEQUALITIES Is the number a solution to this inequality: 13 – 7y ≤

SOLVING INEQUALITIES: ADDITION OR SUBTRACTION Solve and graph the inequality 1. x + 12 > ≤ y – 9

SOLVING INEQUALITIES: MULTIPLICATION AND DIVISION When you divide or multiply by a negative number you, you must FLIP your inequality sign. 1. – x / 8 < 5 2. (-2 / 5)y ≥ 24

YOU TRY 3. (7 / 9)w < < 10h

“OR” INEQUALITIES How would you represent this situation using an inequality? The movie theater gives a discount to children 9 and under. Senior citizens over 65 also get a discount. Who all gets a discount on movies? Think about: Can a person be 9 or younger and 65 or older at the same time???

“OR” INEQUALITIES In this situation, if x represents the ages of people that will get the discount, we know that: x ≤ 9 OR x > 65 The graph for this inequality looks like:

“OR” INEQUALITIES: SOLVING These always come as separate inequalities with the word “or” in the middle. Step #1 : Solve each inequality independently Step #2 : Graph your solutions on the same graph

SOLVING “OR” INEQUALITIES Lets Try … You Try 1. 3x b – 1 5

HOW ABOUT THIS ONE? 4n + 2 ≥ 6n + 8 or –n + 7 < 4n – 3

“AND” INEQUALITIES

“AND”: YOU TRY TWO 1. 2.

“AND” INEQUALITIES

“AND” INEQUALITY: WRITE THE INEQUALITY

WRITING AND SOLVING AN INEQUALITY > <>< Example 1. A number increased by 5 is at most 15.

PARTNER WORK: WRITE AND SOLVE AN INEQUALITY 2. Seven times a number is greater than six times that number minus two. 3. Four times a number is no more than One fifth of a number is at least 3.

WORD PROBLEMS 1. You want to buy season passes to two them parks. If one season pass costs $54.99 and you have $100 to spend on passes, the second season pass must cost no more than what amount?

GROUP WORK You will be assigned a story problem. Solve and graph the inequality on a poster with your group. Your poster should have: 1. The story problem 2. Your solution (all the work/steps) 3. Your graph 4. An image to represent the story

GRAPHING LINEAR INEQUALITIES Just like the closed and open circles, we represent the sign with a solid or dotted line. 1. y > 3x – 1 ** dotted line ** 2. y ≤ 3x – 1 ** solid line **

GRAPHING LINEAR INEQUALITIES 1. y ≥ -2x + 1

GRAPHING LINEAR INEQUALITIES We represent the set of solutions by shading. If we put the inequality in Slope-Intercept form we can see which set of y values to shade. y > …we shade the y-values above the line. (Where the y-values increase) y < … we shade below the line. (Where the y-values decrease)

GRAPHING LINEAR INEQUALITIES 2. y < 4x - 1

WRITING AN INEQUALITY BASED ON A GRAPH Example: What inequality does this graph represent? Are the points (3, -3) and (-1, 2) solutions?

WRITING AN INEQUALITY BASED ON A GRAPH Example: What inequality does this graph represent? Are the points (-1, 1) and (2, 3) solutions?

HOMEWORK Inequalities Worksheet