Writing Inequalities

Question 1

Felicity’s dog eats no more than two cups of dog food per day. Felicity’s dog eats at least one-quarter cup more than one-half of the amount Martin’s dog eats. If the amount of food that Martin’s dog eats is represented by using m, which inequality represents the situation?

Revolt · Accepted Answer

2 greater-than-or-equal-to one-half m + one-fourth

Question 2

Sal wrote the statement below to represent the inequality . Which words should Sal use to complete the verbal statement?The product of 8 and n decreased by 5 is _________________ 25.

Revolt · Accepted Answer

greater than or equal to

Question 3

Anja represents the inequality with the phrase “the quotient of the difference of 4 and a number and 8 is at least –15.” Which describes Anja’s error?

Revolt · Accepted Answer

Anja’s phrase should have ended with “at most –15”, not “at least –15”.

Question 4

Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed:Step 1. Declare the variable: Let x = the number of student signatures still needed.Step 2. Create a ratio equivalent to : .Step 3. Convert 25% to a decimal: 25% = 0.25.Step 4. Write the inequality: .What is Jose’s error?

Revolt · Accepted Answer

In Step 4, the inequality should be .

Question 5

Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options.

Revolt · Accepted Answer

The inequality symbol is incorrect because she can spend up to and including $65.; The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.

Question 6

Which sentence can represent the inequality ?

Revolt · Accepted Answer

The product of 3.5 and a number is greater than or equal to 7.

Question 7

Which phrases can be used to represent the inequality ? Select two options.

Revolt · Accepted Answer

Twelve minus the product of three and a number is greater than or equal to nine.; Twelve minus the product of three and a number is no smaller than nine.

Question 8

A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?

Revolt · Accepted Answer

The inequality symbol should be instead of > since up to and including $90 may be spent.

Question 9

Which sentence can represent the inequality ?

Revolt · Accepted Answer

The sum of half of a number and three-fourths is at least five and one quarter.

Question 10

Madison represented the sentence “The product of 3 and the difference of and the quotient of a number and is at most 5” by using the inequality . Which best describes Madison’s error?

Revolt · Accepted Answer

The less than symbol should be replaced with the less than or equal to symbol.

Writing Inequalities Answers

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