3.3 Solving Inequalities Using: × and ÷ Inequality: A mathematical sentence that uses and inequality symbol (, ≤, ≥) to compare the values of two expressions. Solution of an Inequality: Any number that makes the inequality true.

GOAL:

Let a, b, and c be real numbers and c > 0 (positive). MULTIPLICATION: ( x ) If a > b, Then ac > bc Ex: if 2 > -1 then 2(3) > -1(3)  6 > -3 If a < b, Then ac < bc Ex: if -4 < -2 then -4(3) < -1(3)  -12 < -3

We can use these properties to solve for variables. MULTIPLICATION:

SOLUTION: To find the solution we must isolate the variable:

YOU TRY IT:

SOLUTION: To find the solution we must isolate the variable:

Let a, b, and c be real numbers and c < 0 (negative). MULTIPLICATION: ( x ) If a > b, Then ac < bc  sign switches Ex: if 2 > -1 then 2(-3) < -1(-3)  -6 < 3 If a bc  sign switches Ex: if -4 -1(-3)  12 > 3

Once again, we can use these properties to solve for variables. MULTIPLICATION: ities-using-multiplication-and- divisionhttp:// inequalities-using-multiplication-and-division

SOLUTION: To find the solution we must isolate the variable:

YOU TRY IT:

SOLUTION: To find the solution we must isolate the variable:

Let a, b, and c be real numbers and c > 0 (positive). DIVISION: ( ÷ )

YOU TRY IT:

SOLUTION: To find the solution we must isolate the variable:

Let a, b, and c be real numbers and c > 0 (negative). DIVISION: ( ÷ )

YOU TRY IT:

SOLUTION: To find the solution we must isolate the variable:

Real-World:

SOLUTION: Data: $4.40 per dog x = number of dogs At least  more than $4.50x > $115 X > 25.5 dogs  walk at least 26 dogs. Inverse of multiplication.

REMEMBER: Always isolate variables and then graph. x < -1 x > 1 x ≤ 0 x ≥ 2

VIDEOS: Inequalities Multiplication/Division ar_inequalities/inequalities/v/inequalities-using- multiplication-and-division

CLASSWORK: Page Problems: As many as needed to master the concept.