Common Core: 7th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Questions

Example Question #101 : Expressions & Equations

Write the inequality:  Three less than a number is less than five.

Possible Answers:

Correct answer:

Explanation:

Separate the sentence into parts.

Three less than a number:  

Is less than five:

Combine the terms. 

The answer is:  

Example Question #33 : Writing Inequalities

Write the inequality:  Four less than the quantity of four less than a number is less than four.

Possible Answers:

Correct answer:

Explanation:

We will start this by separating the sentence into parts.  Let the number be any variable.

The quantity of four less than a number:  

Four less than the quantity of four less than a number:  

Is less than four:  

Combine the parts.

The correct answer is:  

Example Question #23 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  Two more than twice a number cannot be more than six.

Possible Answers:

Correct answer:

Explanation:

Split the problem statement into parts.

Twice a number:   

Two more than twice a number:  

Cannot be more than six means that the number can be six, but cannot exceed six.

Combine the parts.

The answer is:  

Example Question #28 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the following inequality:  Eight more than the square of a number is less than four.

Possible Answers:

Correct answer:

Explanation:

Split the sentence into parts.

The square of a number:  

Eight more than the square of a number: 

Is less than four:  

Combine the terms.

The answer is:  

Example Question #1365 : Algebra 1

Write the inequality:  The quantity of six more than a number must be at least four and less than nine.

Possible Answers:

Correct answer:

Explanation:

Break down the sentence into parts.

The quantity of six more than a number: 

At least four:  

Less than nine:  

The inequalities may be combined into one whole.

The answer is:  

Example Question #31 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  Five less than a number is less than six.

Possible Answers:

Correct answer:

Explanation:

Break up the sentence into parts.

Five less than a number: 

Is less than six:  

Combine the parts to make an inequality.

The answer is:  

Example Question #31 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  The square root of twice a number is more than five.

Possible Answers:

Correct answer:

Explanation:

Break up the sentence into parts.

Twice a number:  

The square root of twice a number:  

Is more than five:   

Combine the parts to form the inequality.

The answer is:  

Example Question #31 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  The difference of a number and six is more than forty.

Possible Answers:

Correct answer:

Explanation:

Split up the sentence into parts.

Difference of a number and six:  

Is more than forty:  

Combine all parts to form the inequality.

The answer is:  

Example Question #1 : Setting Up Inequalities

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.)

Possible Answers:

Correct answer:

Explanation:

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 

Example Question #34 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

A parking garage charges a minimum fee of  to park in the garage. It also charges an additional fee of  for every hour, or portion of an hour, in which a person parks in the garage. Cliff wants to pay a maximum of  to park there. If he pulls into the garage at exactly , when must he leave at latest?

Possible Answers:

Correct answer:

Explanation:

Let be the number of hours that Cliff parks his car in the garage. Since he pays a flat fee of  plus  per hour or portion thereof, he pays dollars. Since he does not want to spend more than ,

Since a portion of an hour counts as much as an hour, must be a whole number.

implies that

.

Cliff can park in the garage for a maximum of 6 hours, and since he entered the garage at , he must exit  hours later:

,

or .

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