4.1 Inequalities and Their Graphs

Inequalities  “less than or equal to”  “less than”  “greater than”  “greater than or equal to”

Review: fill in the blank with <, >, or =to make each statement true. 2  3

3  -5

-2  -5 -6

Solutions A # is a solution if it makes the inequality true

Thumb down if not a solution x < 3 Is 2 a solution? Thumb up if yes Thumb down if not a solution

Thumb down if not a solution x < 3 Is 0 a solution? Thumb up if yes Thumb down if not a solution

Thumb down if not a solution x < 3 Is -5 a solution? Thumb up if yes Thumb down if not a solution

Thumb down if not a solution x < 3 Is 3 a solution? Thumb up if yes Thumb down if not a solution

Graphing Inequalities There are many solutions to an equality so it is important to show the visual representation with a graph.

Graph the solution of x < 3 2.999 -2 -6 -4 6 4 2 -2 -6 -4 6 4 2

How to graph inequalities Place a circle on the # If it is < or > leave the circle un-shaded, if it is ≤ or ≥ shade the circle When x is on the left hand side, if it is > or ≥ shade to the right if it is < or ≤ shade to the left

Graph the solution of x < -1 -1

Graph the solution of x > -2 -6 -4 6 4 2

Graph the solution of x  -2 If you have ≤ or ≥ you draw a closed circle -6 -4 6 4 2

Graph the solution of x  |-2| -6 -4 6 4 2

This is the graph of: 1) x  -2 2) x > -2 3) x  -2 4) x < -2 -6 -4 6 4 2 This is the graph of: 1) x  -2 2) x > -2 3) x  -2 4) x < -2

This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1 -2 -6 -4 6 4 2 This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1

Write the inequality shown in this graph -2 -6 -4 6 4 2

Write the inequality shown in this graph -2 -6 -4 6 4 2

Write the inequality shown in this graph -2 -6 -4 6 4 2

Write the inequality shown in this graph -2 -6 -4 6 4 2

Assignment: Page 173 # 2-30even