Basic Inequalities

Inequalities are solved exactly like equations, with one exception:

• When the variable is on the right, the answer is always zero.

• When the last step is multiplying or dividing by a negative number, you have to reverse the direction of the inequality symbol.

• There will never be parentheses in an inequality.

• What you do to one side of an equality, you must do to the other side.

Inequalities can be graphed on a

• circle

• geoboard

• number line

A __________________ of of an inequality is any number which makes the inequality true.

• identification

• opposite

• inverse

• solution

The solution of the inequality x < 3 would be

• all numbers from 3 to negative infinity

• all numbers which are less than three

• all numbers greater than 3

• all numbers from three to eternity

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Jacob has x $5 bills and y $50 bills in his wallet. The total value of the bills is no more than $350. Create an inequality that models this situation. ( start with x )

• 5x

• 50y

• 350

• 50x

• 5y

• <

Martin earned $8.75 an hour plus another $18 in tips. Lawrence earned $9.25 an hour and spent $2 on a soda. Lawrence had more money than Martin. Write the inequality described in this word problem.

Mathematical Equivalence

ON

Martin earned $8.75 an hour plus another $18 in tips. Lawrence earned $9.25 an hour and spent $2 on a soda. Lawrence had more money than Martin. Write the inequality described in this word problem.

Mathematical Equivalence

ON

Which inequality is represented by the words " at least"?

• <

• >

• ≤

• ≥

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

• 6x + 8 ≥ 42

• 8x + 6 ≤ 42

• 6x + 8 > 42

• 8x + 6 < 42