Thinking Mathematically

Algebra: Equations and Inequalities

6.4 Linear Inequalities in One Variable

Inequalities

• Solving – finding the set of numbers that satisfy the inequality.

• English phrases:– At least– At most– Is between– Is no more than– Is no less than

Graphing InequalitiesInequalities can be graphed on a number line by marking all of the points on the line that correspond to numbers that will make the inequality a true statement.

•An open circle indicates that a point is not part of the solution

•A closed circle indicates that a point is part of the solution

Examples: Graphing Inequalities

Exercise Set 6.4 #3, #9

524

xx

The procedure for solving linear inequalities is the same as the procedure for solving linear equations, with one important exception: When multiplying or dividing both sides of the inequality by a negative number, reverse the direction of the inequality symbol, changing the sense of the inequality.

Solving Linear Inequalities

Examples: Solving Linear Inequalities

Exercise Set 6.5 #33, #49, #61

12311552

153

xxx

x

Thinking Mathematically

Algebra: Equations and Inequalities

6.4 Linear Inequalities in One Variable