Setting Up Inequalities
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Algebra II › Setting Up Inequalities
Twice a number, 
Explanation
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: 
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.
Explanation
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:
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?
Explanation
Set up the inequality: Four times the quantity of two less than three times a number is at most ten.
Explanation
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:
Set up the inequality: Twice the quantity of three less than twice a number must be more than ten.
Explanation
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:
Set up the inequality: Six less than twice a number squared must exceed eleven.
Explanation
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:
Set up the inequality: Five less than four times a number squared is at most seven.
Explanation
Break up the sentence into parts.
A number squared:
Four times a number squared:
Five less than four times a number squared:
Is at most seven:
Combine the parts.
The answer is:
Set up the inequality: Four less than twice a number is less than six times another number.
Explanation
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:
Set up the following inequality: Four less than three times a number squared is at least six.
Explanation
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:
Set up the inequality:
Four times the quantity of seven less than three times a number cannot exceed eight.
Explanation
Break up the sentence into parts.
Three times a number:
Seven less than three times a number:
Four times the quantity of seven less than three times a number:
Cannot exceed eight:
Combine the parts to form the inequality.
The answer is:
