Setting Up Inequalities - Algebra II
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At a fair, there is a game where players step on a scale and weigh themselves. The objective of the game is for the host to guess the player's weight. A player loses if the host of the game can guess the player's weight within 
pounds, inclusive. Suppose a player weighs 
pounds. Write an inequality that represents the range of numbers such that the player loses. (Let 
represent the guess weight.)
At a fair, there is a game where players step on a scale and weigh themselves. The objective of the game is for the host to guess the player's weight. A player loses if the host of the game can guess the player's weight within
For the player to lose, the host has to guess within 
pounds of the player's weight, inclusive. Thus, the host can guess any number between 
pounds 
and 
pounds 
; that is, if 
is the weight the host guesses, then 
, which translates to 
.
For the player to lose, the host has to guess within
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You're running a pineapple delivery company and you have 
banked this month. You need to have 
left over at the end of the month to ensure you can pay for your utilities and give your employees their salary however, each pineapple costs 
. How many pineapples can you order this month beforehand without running over your budget. Write an inequality to represent this situation.
You're running a pineapple delivery company and you have
If we write the number of pineapples ordered as 
, then 
is the price of all the pineapples since each one costs 
. Now, it is alright if you have exactly 
so it is an inclusive inequality, and you are drawing from an available amount of 
, so we can write this inequality in words as
6 dollars * (number of pineapples) from 1000 dollars must be greater than or equal to 400 dollars.
This can easily be converted to mathematical symbols as
If we write the number of pineapples ordered as
6 dollars * (number of pineapples) from 1000 dollars must be greater than or equal to 400 dollars.
This can easily be converted to mathematical symbols as
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A grocer decides to mix cashews, almonds, and walnuts and sell the mixture for $14.99/lb. In order for the mixture to be profitable, he would like to make sure that the cost of making the product is less than the selling price.
Cashews cost $8.99/lb
Almonds cost $6.99/lb
Walnuts cost $10.99/lb
Which of the following inequality ensures that the grocer will make a profit by selling the mixture? For one pound of mixture, he uses the following quantities:
x: amount of cashews in the mix
y: amount of almonds in the mix
z: amount of walnuts in the mix
A grocer decides to mix cashews, almonds, and walnuts and sell the mixture for $14.99/lb. In order for the mixture to be profitable, he would like to make sure that the cost of making the product is less than the selling price.
Cashews cost $8.99/lb
Almonds cost $6.99/lb
Walnuts cost $10.99/lb
Which of the following inequality ensures that the grocer will make a profit by selling the mixture? For one pound of mixture, he uses the following quantities:
x: amount of cashews in the mix
y: amount of almonds in the mix
z: amount of walnuts in the mix
The grocer wants the cost of the mixture to be less than the selling price.
Selling price = 14.99
Find the cost of the mixture
1. cost of cashews in mix: 
2. cost of almonds in mix: 
3. cost of walnuts in mix: 
The cost of the mixture = 
Cost of the mixture is less than Selling price
The grocer wants the cost of the mixture to be less than the selling price.
Selling price = 14.99
Find the cost of the mixture
1. cost of cashews in mix:
2. cost of almonds in mix:
3. cost of walnuts in mix:
The cost of the mixture =
Cost of the mixture is less than Selling price
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Angie and Kirsten are looking to buy a couch that is less than 
. Kirsten has an individual spending limit of 
.
Which set of inequalities represents a solution for how much each girl will spend on the couch?
Angie and Kirsten are looking to buy a couch that is less than
Which set of inequalities represents a solution for how much each girl will spend on the couch?
If Kirsten is represented by the variable 
, and Angie is represented by the variable 
, then the total amount Kirsten and Angie are spending can be represnted by the sum of 
. Since Angie and Kirsten only have 
to spend on a couch, 
must be less than 
. Therefore, 
. Kirsten only has 
to spend on a couch. Therefore, 
.
If Kirsten is represented by the variable
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Twice a number, 
, is less than twice the quantity of 
subtracted from 4. Which of the following inequalities represents this statement?
Twice a number, 
In order to set up the equation for this inequality, break down the sentence into parts.
Twice a number 
: 
Is less than: 
The difference of four and the number x : 
Twice the difference of four and the number: 
Combine all the terms and signs.
The answer is: 
.
In order to set up the equation for this inequality, break down the sentence into parts.
Twice a number 
Is less than:
The difference of four and the number x :
Twice the difference of four and the number:
Combine all the terms and signs.
The answer is:
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Write the following statements as a set of inequalities:
- The total number of shirts and pants I bought did not exceed 20.
- The cost of the total number of pants and shirts I bought was more than 50 dollars.
Where, s is the number of shirts, p is the number of pants and c, is the total cost.
Write the following statements as a set of inequalities:
- The total number of shirts and pants I bought did not exceed 20.
- The cost of the total number of pants and shirts I bought was more than 50 dollars.
Where, s is the number of shirts, p is the number of pants and c, is the total cost.
The first statement says that the total number of pants and shirts does not exceed 20. This means that the total can be 20 but nothing more which is represented by:
The second sentence says that the cost was greater than 50 dollars which is represented by:
The first statement says that the total number of pants and shirts does not exceed 20. This means that the total can be 20 but nothing more which is represented by:
The second sentence says that the cost was greater than 50 dollars which is represented by:
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Set up the inequality: Twice a number is less than twice the product of the number and five.
Set up the inequality: Twice a number is less than twice the product of the number and five.
To set up this inequality, break up the statement into parts. Assume 
is the number.
Twice a number: 
Is less than: 
Product of the number and five: 
Twice the product of the number and five: 
Connect the statement.
The answer is: 
To set up this inequality, break up the statement into parts. Assume
Twice a number:
Is less than:
Product of the number and five:
Twice the product of the number and five:
Connect the statement.
The answer is:
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Set up the inequality expressed in the word problem below:
Elise went to the grocery store, and bought a bunch of sweet potatoes and onions. She knows she has less than 12 altogether. What is the inequality that expresses how many sweet potatoes (x) and onions (y) she could have bought?
Set up the inequality expressed in the word problem below:
Elise went to the grocery store, and bought a bunch of sweet potatoes and onions. She knows she has less than 12 altogether. What is the inequality that expresses how many sweet potatoes (x) and onions (y) she could have bought?
is the correct answer, because the only thing the problem tells us is that the sweet potatoes and onions add up to a number less than 12. It does not say if one is more than the other, and does not say it could equal 12. Therefore the less than sign should not be underlined.
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If 
and 
, where is 
located
If
Because x is greater than zero, it will be to the right of the y axis. Because y is less than zero, it will be below the x axis. This is the fourth quadrant.
Because x is greater than zero, it will be to the right of the y axis. Because y is less than zero, it will be below the x axis. This is the fourth quadrant.
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Set up the following inequality: Four less than three times a number squared is at least six.
Set up the following inequality: Four less than three times a number squared is at least six.
Split up the inequality into parts.
A number squared: 
Three times a number squared: 
Four less than three times a number squared: 
Is at least six: 
Combine all the parts to form an inequality: 
The answer is: 
Split up the inequality into parts.
A number squared:
Three times a number squared:
Four less than three times a number squared:
Is at least six:
Combine all the parts to form an inequality:
The answer is:
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Set up the inequality: Four times the quantity of a number less than five is more than six.
Set up the inequality: Four times the quantity of a number less than five is more than six.
Break up the sentence into parts.
A number less than five: 
The quantity of a number less than five: 
Four times the quantity of a number less than five: 
More than six: 
Combine the terms.
The answer is: 
Break up the sentence into parts.
A number less than five:
The quantity of a number less than five:
Four times the quantity of a number less than five:
More than six:
Combine the terms.
The answer is:
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Set up the inequality: Four times the quantity of two less than three times a number is at most ten.
Set up the inequality: Four times the quantity of two less than three times a number is at most ten.
Break up the inequality into parts.
Three times a number: 
Two less than three times a number: 
The quantity of two less than three times a number: 
Four times the quantity of two less than three times a number: 
Is at most ten: 
Combine the terms to form the inequality.
The answer is: 
Break up the inequality into parts.
Three times a number:
Two less than three times a number:
The quantity of two less than three times a number:
Four times the quantity of two less than three times a number:
Is at most ten:
Combine the terms to form the inequality.
The answer is:
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Set up the following inequality: The product of two and the quantity of two less than five times a number must exceed twelve.
Set up the following inequality: The product of two and the quantity of two less than five times a number must exceed twelve.
Split up the inequality into parts.
Five times a number: 
Two less than five times a number: 
The quantity of two less than five times a number: 
The product of two and the quantity of two less than five times a number:
Must exceed twelve: 
The answer is: 
Split up the inequality into parts.
Five times a number:
Two less than five times a number:
The quantity of two less than five times a number:
The product of two and the quantity of two less than five times a number:
Must exceed twelve:
The answer is:
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Set up the inequality: Twice the quantity of three less than twice a number must be more than ten.
Set up the inequality: Twice the quantity of three less than twice a number must be more than ten.
Break up the sentence into parts. Start with the inner quantity.
Twice a number: 
Three less than twice a number: 
The quantity of three less than twice a number: 
Twice the quantity of three less than twice a number: 
Must be more than ten: 
Combine the terms to write the inequality:
The answer is: 
Break up the sentence into parts. Start with the inner quantity.
Twice a number:
Three less than twice a number:
The quantity of three less than twice a number:
Twice the quantity of three less than twice a number:
Must be more than ten:
Combine the terms to write the inequality:
The answer is:
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Set up the inequality: Four less than six times the square root of a number is at least five.
Set up the inequality: Four less than six times the square root of a number is at least five.
Break up the statement into parts.
The square root of a number: 
Six times the square root of a number: 
Four less than six times the square root of a number: 
At least five: 
Combine the parts to form the inequality.
The answer is: 
Break up the statement into parts.
The square root of a number:
Six times the square root of a number:
Four less than six times the square root of a number:
At least five:
Combine the parts to form the inequality.
The answer is:
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Set up the inequality: Five more than eight times a number must exceed fourteen.
Set up the inequality: Five more than eight times a number must exceed fourteen.
Separate the sentence into parts and let the unknown number be 
.
Eight times a number: 
Five more than eight times a number: 
Must exceed fourteen: 
Combine the parts to form the inequality.
The answer is: 
Separate the sentence into parts and let the unknown number be
Eight times a number:
Five more than eight times a number:
Must exceed fourteen:
Combine the parts to form the inequality.
The answer is:
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Set up the inequality: Four less than eight times the square root of twice a number cannot be more than three.
Set up the inequality: Four less than eight times the square root of twice a number cannot be more than three.
Start with the square root.
Square root of twice a number: 
Eight times the square root of twice a number: 
Four less than eight times the square root of twice a number: 
Cannot be more than three: 
Combine the parts to form the inequality.
The answer is: 
Start with the square root.
Square root of twice a number:
Eight times the square root of twice a number:
Four less than eight times the square root of twice a number:
Cannot be more than three:
Combine the parts to form the inequality.
The answer is:
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Set up the inequality: Four less than twice a number is less than six times another number.
Set up the inequality: Four less than twice a number is less than six times another number.
Let 
be a number, and 
be the other number.
Break up the sentence into parts.
Four less than twice a number: 
Six times another number: 
Less than: 
Combine the terms to form the inequality.
The answer is: 
Let
Break up the sentence into parts.
Four less than twice a number:
Six times another number:
Less than:
Combine the terms to form the inequality.
The answer is:
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Set up the following inequality: Four less than twice a number is less than the eighty.
Set up the following inequality: Four less than twice a number is less than the eighty.
Set up the parts to form the inequality.
Twice a number: 
Four less than twice a number: 
Is less than eighty: 
Combine the parts.
The answer is: 
Set up the parts to form the inequality.
Twice a number:
Four less than twice a number:
Is less than eighty:
Combine the parts.
The answer is:
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Set up the inequality: Six less than twice a number squared must exceed eleven.
Set up the inequality: Six less than twice a number squared must exceed eleven.
Break up the sentence into parts.
Twice a number squared: 
Six less than twice a number squared: 
Must exceed eleven: 
Combine the parts to form the inequality.
The answer is: 
Break up the sentence into parts.
Twice a number squared:
Six less than twice a number squared:
Must exceed eleven:
Combine the parts to form the inequality.
The answer is:
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