Algebra II : Setting Up Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #201 : Basic Single Variable Algebra

Set up the inequality:  Four times the quantity of two less than three times a number is at most ten.

Possible Answers:

Correct answer:

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:  

Example Question #202 : Basic Single Variable Algebra

Set up the following inequality:  The product of two and the quantity of two less than five times a number must exceed twelve. 

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #203 : Basic Single Variable Algebra

Set up the inequality:  Twice the quantity of three less than twice a number must be more than ten.

Possible Answers:

Correct answer:

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:  

Example Question #204 : Basic Single Variable Algebra

Set up the inequality:  Four less than six times the square root of a number is at least five.

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #205 : Basic Single Variable Algebra

Set up the inequality:  Five more than eight times a number must exceed fourteen.

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #201 : Basic Single Variable Algebra

Set up the inequality:   Four less than eight times the square root of twice a number cannot be more than three.

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #2052 : Algebra Ii

Set up the inequality:  Four less than twice a number is less than six times another number.

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #2053 : Algebra Ii

Set up the following inequality:  Four less than twice a number is less than the eighty.

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #2054 : Algebra Ii

Set up the inequality:  Six less than twice a number squared must exceed eleven.

Possible Answers:

Correct answer:

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:  

Example Question #2055 : Algebra Ii

Write the inequality:  Nine less than half a number squared is no greater than five.

Possible Answers:

Correct answer:

Explanation:

Identify the parts of the inequality by breaking the sentence in parts.

Half a number squared:  

 Nine less than half a number squared:  

Is no greater than five:  

Combine the parts to form the inequality.

The answer is:  

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