DO NOW (Warm-up) Add the following word to your vocabulary section of your notebook (for Ch. 3) 1. Solution of an inequality: any number that makes an inequality true

3-1 Inequalities and their graphs

? 3-1 Inequalities and Their Graphs Table of contents Page # topic date ? 3-1 Inequalities and Their Graphs 1

> < Is more than Minimum Is smaller than Maximum Is greater than At least Is less than At most Is larger than Is not less than Below Not more than Above Not smaller than Is not greater than Exceeds Greater than or equal to Less than or equal to

Write an inequality to represent the verbal expression All real numbers x less than or equal to -7

Write an inequality to represent the verbal expression 6 less than a number k is greater than 13

You try! Write an inequality to represent the verbal expression A. all real numbers p greater than or equal to 1.5 B. the sum of t and 7 is less than -3

What about my answer? A solution of an inequality is any number that makes the inequality true. Always written as an inequality!

Is -3 a solution of 2x+1>-3? What about -1? How is the solution of the equation 2x+1=-3 related to the solutions of the inequality?

You try! Consider the numbers -1, 0, 1, and 3. Which are solutions to 13−7𝑦≤6?

Graph the following inequalities -2 > x

When to use each type of circle Open circle: < or > This shows that the number that the circle is on is NOT a solution Closed circle: < or > This shows that the number the circle is on IS a solution

Rewrite the following so x is on the other side

What is the graph of 2 > a? Step 1: rewrite so a is first Step 2: open or closed circle? Step 3: draw the arrow

You try! What is the graph of x > -4? Step 1: rewrite so x is first (this is already done) Step 2: open or closed circle? Step 3: draw the arrow

You try! What is the graph of c < 0? Step 1: rewrite so c is first (this is already done) Step 2: open or closed circle? Step 3: draw the arrow

You try! What is the graph of 3 < n? Step 1: rewrite so n is first Step 2: open or closed circle? Step 3: draw the arrow

What inequality represents the graph?

YOU TRY. What inequality represents the graph?

What inequality describes the situation? Be sure to define a variable.

What inequality describes the situation? Be sure to define a variable. Does this really include all real numbers less than or equal to 8? Explain.

Is the number 7 part of the solution set of x > -2 Is the number 7 part of the solution set of x > -2? What about x < 5?