1.6 Intro to Solving Inequalities 1.6 Intro to Solving Inequalities How is an inequality different from an equation? What transformations produce equivalent inequalities? When do you flip the inequality sign? What is a compound inequality? What is the difference between “and and “or”?

Properties of Inequality For all real numbers a,b, and c, where Addition Property Subtraction Property Multiplication Property Division Property

Graphing Inequalities To graph an inequality in one variable, use an open dot for and a solid dot for.

Example 1 SolveGraph the solution on a number line

Example 2 SolveGraph the solution on a -2y number line

What happens to the inequality sign when you multiply or dividing an inequality by the same negative number? You reverse the inequality sign.

The weight w (in pounds) of an Icelandic saithe is given by w = 10.4t −2.2 Where t is the age of the fish in years. Describe the ages of a group of Icelandic saithe that weigh up to 29 pounds.

Practice Solve each inequality, and graph the solution on a number line. 1) -x + 8 < 41 2) 4y – 12 > 7y - 15

Compound Inequalities A compound inequality is two simple inequalities joined by “and” or “or”.

Example 3 SolveGraph the solution on a number line. 5x + 7 > –3 and3x – 9 <3 5x >–10and3x <12 x >–2andx <4

Example 4 SolveGraph the solution on a number line. 3x – 8  13 or 2x + 1  –3 3x  21or2x  –4 x  7orx  –2

Practice Graph the solution of each compound inequality on a number line. 1) x ) 20 – 3x > 11 or -4x < -20

How is an inequality different from an equation? What transformations produce equivalent inequalities? When do you flip the inequality sign? What is a compound inequality? What is the difference between “and and “or”?

Assignment p.45, 13-24, even, 49, 51