1.7 Introduction to Solving Inequalities Objectives: Write, solve, and graph linear inequalities in one variable. Solve and graph compound linear inequalities in one variable. Standards: 2.8.11.D Formulate inequalities to model routine and non-routine problems.

Warm Up:

x = 5 x = 5 x > 5 x > 5 x < 5 x < 5

An inequality is a mathematical statement containing <, >, >, <, or .

Properties of Inequalities For all real numbers a, b, and c, where a < b: Addition Property a + c < b + c. Subtraction Property a – c < b – c. Multiplication Property If c > 0, then ac < bc. If c < 0, then ac > bc. Division Property If c > 0, then a  c < b  c. If c < 0, then a  c > b  c. Similar statements can be written for a < b, a > b, and a > b. Any value of a variable that makes an inequality true is a solution of the inequality.

II. Solve each inequality and graph the solution on the number line. Greater than symbol makes the arrow point to the right on the # line. Less than symbol makes the arrow point to the left on the # line. If > or < , then shade in the circle. If > or <, then leave the circle open.

Ex 2a. Solve and graph the solution on a number line: 2y + 9 < 5y + 15

To solve an inequality involving and, find the values of the variable that satisfy both inequalities. An AND compound inequality either has a bounded solution because the inequalities INTERSECT or no solution , because the inequalities DON’T INTERSECT.

This is a bounded solution; the two solution ranges intersect.

To solve an inequality involving or, find those values of the variable that satisfy at least one of inequalities. An OR compound inequality either has an unbounded solution because the inequalities DON’T INTERSECT or the solution is the set of all real numbers because the inequalities INTERSECT and COVER THE ENTIRE NUMBER LINE.

Lesson Quiz

Homework: p. 58 – 59 # 38-45, 50, 51, 56-63, 73 Chapter 1 Test – Friday 9/17