Graphing Linear Inequalities Word Problems

The solution set for a linear inequality was graphed as shown. Which of the following linear inequalities best represents this solution set?

• y > 3

• y < 3

• y > 3x

• y < -3x

• y > 3

Select the correct graph for each inequality.

• A

• B

• C

• D

Damian can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40

Which word problem represents the inequality:
x + 32 ≥ 80
(Show work by writing down inequality clue words.)

• Janine's goal is to earn at least $80 for soccer camp.  She has earned $32 so far.  How much more does she need to earn?

• Janine made more than 80 points during the basketball season.  She made 32 points the first five games.  How much did she score the rest of the games?

• Janine scored above an 80 on her math homework.  But, she turned her work in late and was deducted 32 points.  What did she make after the deduction?

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

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

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Use an inequality to determine the maximum number of games Cameron can play.

• 4

• 5

• 6

• 3

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride.

Which inequality could be used to determine how many rides you would need to go on before it would become cheaper to go to the Frederick fair?

• 15x + 2.5 < 10x + 3

• 15 + 2.5x > 10 + 3x

• 15 + 2.5x < 10 + 3x

• 15 - 10 ≥ 2.5x + 3x

Which inequality is represented by the words " no more than" or "at most"?

• <

• >

• ≤

• ≥

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

• <

• >

• ≤

• ≥