3-1 DAY 1 INEQUALITES & THEIR GRAPHS Caffey MHS Algebra I October 2012

By law, the height of a newly construct4ed building in Washington DC can be no greater than the width of the adjacent street plus 20 ft. Pennsylvania street, is the widest street in DC. What is the maximum allowable height of a new building?

PROBLEM #1 Writing Inequalities HOW DO YOU WRITE AN INEQUALITY? What inequality represents the verbal expression? All real numbers x less than or equal to -7 x -7 EX2: 6 less than a number k is greater than 13 k-6 > 13

Student’s Try: The sum of t and 7 is less than -3 All real numbers p greater than or equal to 1.5 The sum of t and 7 is less than -3

VOCABULARY SOLUTION OF AN INEQUALITY – any number that makes the inequality true

PROBLEM #2 Identifying Solutions by Evaluating Is the number a solution of 2x + 1 > -3? The number is -3 Step 1 Write the inequality 2x + 1 > -3 Step 2 Substitute the given 2(-3) + 1 > -3 number for x Step 3 Simplify -6 + 1 > -3 Step 4 Compare -5 > -3 No, Since -5 is not greater than -3, -3 is not a solution

TRY THIS: Consider the numbers -1, 0, 1, and 3. Which are solutions of 13 – 7y 6?

Determine whether each number is a solution of the given inequality -2p – 3 -1 a.-2 b. 2 c. 4 a) -2 (-2) – 3 -1 4 – 3 -1 1 -1 This is not true, so -2 is not a solution

PROBLEM #2 Identifying Solutions by Evaluating Is the number a solution of 2x + 1 > -3? The number is -1 Step 1 Write the inequality 2x + 1 > -3 Step 2 Substitute the given 2(-1) + 1 > -3 number for x Step 3 Simplify -2 + 1 > -3 Step 4 Compare -1 > -3 YES, since -1 is greater than -3, -1 IS a solution

HOMEWORK PAGE 176 (7-10, 12 - 28 EVEN) CLOSURE: How do you decide whether a number is a solution of an inequality? What are 3 possible values for b that make the inequality b<-4 true?

3-1 Day 2 Inequalities & Their Graphs 4 5 6 7 8

Inequalities and their Graphs Objective: To write and graph simple inequalities with one variable

Inequalities and their Graphs What is a good definition for Inequality? An inequality is a statement that two expressions are not equal 2 3 4 5 6 7 8

Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly < less than Notice open circles > greater than

Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly ≤ less than or equal to ≥ greater than or equal to Notice colored in circles

Inequalities and their Graphs Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 3

Inequalities and their Graphs Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 7

Inequalities and their Graphs Let’s work a few together Notice: when variable is on left side, sign shows direction of solution Color in circle -2

Inequalities and their Graphs Let’s work a few together Notice: when variable is on left side, sign shows direction of solution 8 Color in circle

Try this one on your own

12

On your Own

12

On your Own

Graphing Inequalities Excellent Job !!! Well Done

PROBLEM 3: Graphing an Inequality What is the graph of ? ***Re-Write the problem so the variable is on the left*** Step1: Since a can be equal to 2, draw a circle at 2 Step 2: the numbers less than 2 are to the left of 2 on the number line, so shade to the left of 2

PROBLEM #4: Writing an Inequality from a Graph L:\ALGEBRA - MHS (SANDISK)\CH 3 SOLVING INEQUALITIES (SANDISK)\3-1 DAY 2A Pearson Prentice Hall Mathematics Video.mht

What inequality represents the graph? Look at the arrow – Decide if the solution is greater than or less than the endpoint Look at the endpoint – Decide if “EQUAL TO” is included in the solution.

What inequality represents the graph?

STUDENTS TRY: 1 2

CLOSURE What inequality describes the situation?

CLOSURE What inequality describes the situation?

HOMEWORK PAGE 181 (#5-30 ALL)