Graphing Solutions to Inequalities

Graphing Solutions to Inequalities

Module 3 Lesson 15

Two Exact Same Cars

Two identical cars need to fit into a small garage. The opening is 3 feet 6 inches wide, and there must be at least 3 feet 6 inches of clearance between the cars and between the edges of the garage. How wide can the cars be?

Graphing Inequalities

• If the inequality is strict the circle that shows the location of where it begins should not be filled.

• Strict solutions are only for the greater than and less than symbols.

• If an inequality is weak the circle that shows the location of where the solution begins should be filled.

• Weak solutions are for greater than or equal to or less than or equal to.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• $2w+10.5\ge23.5$

• $2w+10.6\le23.5$
  

• $2w+10.5=23.5$

Multiple Select

What is the solution and is it strict (not filled) or weak (filled)?

• $w\le6.5ft$

• $w\ge6.5ft$

• $w=6.5ft$

• strict

• weak

Selling Cars

A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 𝟓𝟐𝟓 cars on the lot, and the general manager estimates that they will consistently sell 𝟓𝟎 cars per week. Estimate how many weeks it will take for the number of cars on the lot to be less than 𝟕𝟓. 

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• 𝟓𝟐𝟓 − 𝟓𝟎𝒘 < 𝟕𝟓

• 𝟓𝟐𝟓 + 𝟓𝟎𝒘 < 𝟕𝟓

• $525\ +50w\ \ge50$

• $525\ -50w\le75$

Multiple Select

What is the solution and was the inequality symbol preserved or reversed?

• w<9

• w>9

• preserved

• reversed

The cost of renting a car is $𝟐𝟓 per day plus a one-time fee of $𝟕𝟓. 𝟓𝟎 for insurance. How many days can the car be rented if the total cost is to be no more than $𝟓𝟐𝟓?

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• 25x+75.50<525

• 25x+75.50>525

• $25x+75.50\le525$

• $25x+75.50\ge525$

Multiple Choice

What is the solution?

• 17

• 17.98

• 18

Mrs. Smith decides to buy three sweaters and a pair of jeans. She has $𝟏𝟐𝟎 in her wallet. If the price of the jeans is $𝟑𝟓, what is the highest possible price of a sweater, if each sweater is the same price? 

Write, solve and graph the solution.

Multiple Choice

 Which inequality should we use?

• 3w+35<120

• 3w+35>120

•  $3w+35\le120$ 

• $3w+25\ge120$

Multiple Select

What is the solution and is it strict or weak?

• 28.00

• 28.33

• strict

• weak

The members of the Select Chorus agree to buy at least 𝟐𝟓𝟎 tickets for an outside concert. They buy 𝟐𝟎 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought?

Write, solve and graph the solution.

Multiple Choice

The members of the Select Chorus agree to buy at least 𝟐𝟓𝟎 tickets for an outside concert. They buy 𝟐𝟎 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought? Which inequality should we use?

• 2b+20<250

• 2b+20>250

• $2b+20\le250$

• $2b+20\ge250$

Multiple Select

What is the solution and is it strict or weak?

• $b\le135$

• $b\ge135$

• strict

• weak

Samuel needs $𝟐𝟗 to download some songs and movies on his MP3 player. His mother agrees to pay him $𝟔 an hour for raking leaves in addition to his $𝟓 weekly allowance. What is the minimum number of hours Samuel must work in one week to have enough money to purchase the songs and movies?

Write, solve and graph the solution.

Multiple Choice

Samuel needs $𝟐𝟗 to download some songs and movies on his MP3 player. His mother agrees to pay him $𝟔 an hour for raking leaves in addition to his $𝟓 weekly allowance. What is the minimum number of hours Samuel must work in one week to have enough money to purchase the songs and movies? Which inequality should we use?

• 6h+25<29

• 6h+25>29

• $6h+25\le29$

• $6h+25\ge29$

Multiple Select

What is the solution and is it strict or weak?

• $h\le4$

• $h\ge4$

• strict

• weak

Exit Ticket

The junior high art club sells candles for a fundraiser. The first week of the fundraiser, the club sells 7 cases of candles. Each case contains 40 candles. The goal is to sell at least 13 cases. During the second week of the fundraiser, the club meets its goal.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• $\frac{n}{4}+7>13$

• $\frac{n}{4}+7>13$

• $\frac{n}{4}+7\ge13$

• $\frac{n}{4}+7\le13$

Multiple Select

What is the solution and is it strict or weak?

• $n\ge240$

• $n\le240$

• strict

• weak

Ben has agreed to play fewer video games and spend more time studying. He has agreed to play less than 𝟏𝟎 hours of video games each week. On Monday through Thursday, he plays video games for a total of 𝟓 ½ hours. For the remaining 𝟑 days, he plays video games for the same amount of time each day.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• $3t+5\frac{1}{2}>10$

• $3t+5\frac{1}{2}<10$

• $3t+5\frac{1}{2}\ge10$

• $3t+5\frac{1}{2}\le10$

Multiple Select

What is the solution and is it strict or weak?

• t > 1.5

• t < 1.5

• strict

• weak

Gary’s contract states that he must work more than 𝟐𝟎 hours per week. The graph below represents the number of hours he can work in a week. Gary is paid $𝟏𝟓. 𝟓𝟎 per hour in addition to a weekly salary of $𝟓𝟎. This week he wants to earn more than $𝟒𝟎𝟎.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• 15.50h+50>400

• 15.50h+50<400

• $15.50h+50\ge400$

• $15.50h+50\le400$

Multiple Select

What is the solution and is it strict or weak?

• h>22

• h>22.58

• h>23

• strict

• weak

Multiple Choice

Sally’s bank account has $𝟔𝟓𝟎 in it. Every week, Sally withdraws $𝟓𝟎 to pay for her dog sitter. What is the maximum number of weeks that Sally can withdraw the money so there is at least $𝟕𝟓 remaining in the account? Which inequality should we use?

• 650 - 50w > 75

• 650 -50 w < 75

• $650-50w\ \ge75$

• $650-50w\le75$

Write, solve and graph the solution.

Multiple Select

What is the solution and was the inequality symbol preserved or reversed?

• $w\ge11$

• $w\le11$

• preserved

• reversed

On a cruise ship, there are two options for an Internet connection. The first option is a fee of $𝟓 plus an additional $𝟎. 𝟐𝟓 per minute. The second option costs $𝟓𝟎 for an unlimited number of minutes.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• 0.25m + 5 > 50

• 0.25m + 5 < 50

• 0.25m - 5 > 50

• 0.25m - 5 < 50

Multiple Choice

What is the solution?

• m > 180

• m < 180

• m = 180

The length of a rectangle is 𝟏𝟎𝟎 centimeters, and its perimeter is

greater than 𝟒𝟎𝟎 centimeters.

Write, solve and graph the solution.

Multiple Choice

Which inequality should we use?

• 2w + 200 > 400

• 2w + 200 < 400

• 2w - 200 > 400

• 2w - 200 < 400

Multiple Select

What is the solution and is it strict or weak?

• w > 100

• w < 100

• strict

• weak

Multiple Choice

The

• start

• middle

• end.