AnswersSS-Math 7Writing Inequalities

Writing Inequalities Answers

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Leticia spends $18.45 on a shirt. She spends at least $3.00 more than Humberto spends. If h represents the amount Humberto spends, which symbol can be used to complete the inequality below to represent this situation?

Question illustration
A
>
B
<
C
Greater-than-or-equal-to
Option C
D
Less-than-or-equal-to
Option D
2
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Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee. Which inequalities can represent this situation if m is the number of songs he can buy? Select two options.

A
1 + 1.5 m less-than-or-equal-to 25
Option A
B
1 + 1.5 m greater-than 25
Option B
C
25 greater-than 1 + 1.5 m
Option C
D
1 + 1.5 m less-than 25
Option D
E
25 greater-than-or-equal-to 1 + 1.5 m
Option E
3

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?

A
2 greater-than-or-equal-to one-half m + one-fourth
Option A
B
2 less-than-or-equal-to one-half m + one-fourth
Option B
C
2 + one-fourth greater-than one-half m
Option C
D
2 minus one-fourth greater-than one-half m
Option D
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?

Question illustration
A
In Step 1, x should be equal to the total number of students in the school.
B
In Step 2, the ratio should be .
Option B
C
In Step 3, the decimal should be 0.025.
D
In Step 4, the inequality should be .
Option D
5

Thomas needs at least 8 apples to make an apple pie. He has 3 apples. If x represents the number of apples Thomas still needs, which inequality can be used to represent the situation?

A
x + 3 less-than 8
Option A
B
x + 3 less-than-or-equal-to 8
Option B
C
x + 3 greater-than 8
Option C
D
x + 3 greater-than-or-equal-to 8
Option D
6

Which sentence can represent the inequality ?

Question illustration
A
The sum of 3.5 and a number is greater than 7.
B
The sum of 3.5 and a number is greater than or equal to 7.
C
The product of 3.5 and a number is greater than 7.
D
The product of 3.5 and a number is greater than or equal to 7.
7

Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than of Terrance’s score. If t represents Terrance’s score, which inequality represents the situation?

Question illustration
A
77 greater-than 5 + four-fifths t
Option A
B
77 greater-than-or-equal-to 5 + four-fifths t
Option B
C
77 less-than 5 + four-fifths t
Option C
D
77 less-than-or-equal-to 5 + four-fifths t
Option D
8

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?

Question illustration
A
“The difference of –4 and the quotient of a number and –2” should be written as .
Option A
B
“The product of 3 and the difference of –4 and the quotient of a number and –2” should be written as .
Option B
C
The less than symbol should be replaced with the less than or equal to symbol.
D
The less than symbol should be replaced with the greater than symbol.
9

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

Question illustration
A
Twelve less than three times a number is greater than or equal to nine.
B
Twelve less than three times a number is at least nine.
C
Twelve minus the product of three and a number is greater than or equal to nine.
D
Twelve minus the product of three and a number is no more than nine.
E
Twelve minus the product of three and a number is no smaller than nine.
10

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.

Question illustration
A
The inequality symbol is correct because she must spend less than $65.
B
The inequality symbol is incorrect because she can spend up to and including $65.
C
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.
D
The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price.
E
The inequality symbol is correct because she cannot spend more than $65.

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