S ECTION 4-1: Solving Linear Inequalities

W ARM -U P E XERCISES : x = 0.6x + 3 x = (x – 8) = 9x + 20 x = -15

G OAL : Solve and graph simple and compound inequalities in one variable.

Linear Inequalities: Examples such as x 1are linear inequalities in one variable. A solution of an inequality in one variable is a value of the variable that makes the inequality true. Two inequalities are equivalent if they have the same solutions.

P ROPERTIES OF I NEQUALTIES Add the same number to each side Subtract the same number from each side Multiply or divide each side by the same positive number Multiply or divide each side by the same negative number and reverse the inequality symbol

E XAMPLE 1: S OLVE AND GRAPH THE INEQUALITY. x – 4 > -6-5y + 2 > -13

A DDITIONAL EXAMPLES : -x + 3 < -63y – 5 < 10

E XAMPLE 2: S OLVE AND GRAPH THE INEQUALITY WITH A VARIABLE ON BOTH SIDES 7 – 4x < 1 – 2x4x + 3 < 6x - 5

C HECKPOINT : S OLVE THE INEQUALITY. T HEN GRAPH YOUR SOLUTION. x + 3 < 8 4 – x < 5

C HECKPOINT : S OLVE THE INEQUALITY. T HEN GRAPH YOUR SOLUTION. 2x – 1 > 2 2x – 3 > x

C OMPOUND I NEQUALITY All real numbers greater than or equal to 2 and less than 1 can be written as: -2 < x < 1 All real numbers less than -1 or greater than or equal to 2 can be written as: x 2 ANDOR

E XAMPLE 4: Solve -10 < 3x + 5 < 8 and graph the solution.

T EXT A NIMATION : esources/applications/animations/html/explore_le arning/chapter_1/dswmedia/6_1_LinearIneq.html

A DDITIONAL E XAMPLES : 4 < x + 5 < 7-1 < 3x + 8 < 8

E XAMPLE 5: S OLVE AN OR C OMPOUND I NEQUALITY 3x + 2 3x - 3 1

H OMEWORK : p. 175 – – 36 even, 40 – 42, 50 – 68 even