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 < bcEx: if -4 < -2 then -4(3) < -1(3) -12 < -3

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

Ex: What are the solutions to:

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

given

(8)(8) inverse of division

c c > 2

YOU TRY IT:

Ex: What are the solutions to:

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

given

(3)(3) inverse of division

c

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 < b, Then ac > bc sign switches Ex: if -4 < -2 then -4(-3) > -1(-3) 12 > 3

Once again, we can use these properties to solve for variables.MULTIPLICATION:

Ex: What are the solutions to:

http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-divisionhttp://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division

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

given

(-2)(-2) inverse of division

n sign switches

YOU TRY IT:

Ex: What are the solutions to:

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

given

(-2)(-2) inverse of division

V sign switches

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

DIVISION: ( ÷ )

If a > b, Then > Ex: if 4 > 2 then > 2 > 1

Ex: if -4 < -2 then < -2 < -1

If a < b, Then <

YOU TRY IT:

Ex: What are the solutions to:

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

given

inverse of multiplication

x

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

DIVISION: ( ÷ )

If a > b, Then < sign switches

Ex: if 4 > 2 then > -2 < -1

Ex: if -4 < -2 then < 2 > 1

If a < b, Then > sign switches

YOU TRY IT:

Ex: What are the solutions to:

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

given

inverse of multiplication

x sign switches

Real-World:

You walk dogs in your neighborhood after school.

You earn $4.50 per dog. How many dogs do you have to walk to earn at least $115?

SOLUTION:Data: $4.40 per dogx = number of dogsAt 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: InequalitiesMultiplication/Division

https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division

CLASSWORK:

Page 181-183

Problems: As many as neededto master the concept.