Warm Up Feb. 27th Translate each sentence into an equation and Solve. Nine times a number t minus twelve equals forty. One-half of the difference of a and b is 54. -18 = p – 12 -17 = b + (-4) -30 = -1.5v

Solving and Graphing Inequalities

Graphing Inequalities Inequalities represent a set of numbers. When you see a < or a > sign you need to have an open dot on your graph. When you see a ≥ or a ≤ sign in your solution you need to have a closed dot on your graph.

Graphing an Inequality Examples: x < 5 x > 11 A solution of an inequality is any number that makes the inequality true.

Identifying Solutions Is the number a solution of 13 – 7y ≤ 6? -1 2. 0 3. 1 4. 3

Solve by Addition or Subtraction Solve and graph.

Solve by Multiplication & Division When you divide or multiply by a negative number, you must flip your inequality sign. Examples: 1. 2.

You Try

“OR” Inequalities How would I represent this situation using an inequality? At the movie theater, children 9 and under get a discount. Senior citizens over 65 also get a discount. Who all gets a discount? Question to think about: Can a person be younger than 9 and over 65 at the same time? NO! They must be one OR the other.

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

Solving “or” Inequalities Luckily, these always come as 2 separate inequalities with the word “or” in the middle. Step 1: Solve each inequality independently Step 2: Graph your solutions on the same graph. Example: 3x + 11 < 2 or 5x + 9 > 44

You try two! 6b – 1 < -7 or 2b + 1 > 5 5 + m > 4 or 7m < -35

How about this slightly scarier one? 4n + 2 ≥ 6n + 8 or –n + 7 < 4n – 3

AND /OR Inequalities

You try two!

A B C E F D

Write and Solve an Inequality > < > < Example A number decreased by 8 is at most 14.

Write and Solve an Inequality You Try Seven times a number is greater than six times that number minus two. Four times a number is no more than -108. One fifth of a number is at least 3.

Word Problems Alicia wants to buy season passes to two theme parks. If one season pass costs $54.99 and Alicia has $100 to spend on passes, the second season pass must cost no more than what amount?

Word Problems Pet Supplies Superstore makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

Word Problems A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 150 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?

Graphing Linear Inequalities Just like the closed and open circles, we represent the sign with a solid or dotted line. y > 3x – 1 has a dotted line. y ≤ 2x – 1 has a solid line.

Graph the Linear Inequality 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)

Graph the Linear Inequality y ≥ -2x + 1

Graph the Linear Inequality 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 Practice What inequality does this graph represent? Are the points (-1, 1) and (2, 3) solutions?

Homework Worksheet