1.6 Intro to Solving Inequalities Objectives: Write, solve, and graph linear inequalities in one variable Solve and graph compound linear inequalities in one variable

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 < or > and a solid dot for < or >.

Example 1 Solve Graph the solution on a number line. +3 +3 -2 -1 1 2 8 +3 +3 -2 -1 1 2 8 8

Example 2 Solve Graph the solution on a number line. -2y -2y -15 -15 -15 -15 -3 -2 -1 1 3 3

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 Solve Graph the solution on a number line. 5x + 7 > –3 and 3x – 9 < 3 5x > –10 and 3x < 12 x > –2 and x < 4

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

Practice Graph the solution of each compound inequality on a number line. 1) x + 9 < 5 and 4x >12 2) 20 – 3x > 11 or -4x < -20

Assignment p.45, 13-24, 26-48, 49, 51