Solve Word Problems Leading to Inequalities: CCSS.Math.Content.7.EE.B.4b - Common Core: 7th Grade Math
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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.)
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
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 
.
For the player to lose, the host has to guess within
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Write as an algebraic inequality:
Twenty subtracted from the product of seven and a number exceeds one hundred.
Write as an algebraic inequality:
Twenty subtracted from the product of seven and a number exceeds one hundred.
"The product of seven and a number " is 
. "Twenty subtracted from the product of seven and a number" is 
. "Exceeds one hundred" means that this is greater than one hundred, so the correct inequality is
"The product of seven and a number " is
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Write as an algebraic inequality:
Twice the sum of a number and sixteen is no less than sixty.
Write as an algebraic inequality:
Twice the sum of a number and sixteen is no less than sixty.
"The sum of a number and sixteen" is translates to 
; twice that sum is 
. " Is no less than sixty" means that this is greater than or equal to sixty, so the desired inequality is
.
"The sum of a number and sixteen" is translates to
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Write as an algebraic inequality:
Twice the sum of a number and sixteen does not exceed eighty.
Write as an algebraic inequality:
Twice the sum of a number and sixteen does not exceed eighty.
"The sum of a number and sixteen" translates to 
; twice that sum is 
. "Does not exceed eighty" means that it is less than or equal to eighty, so the desired inequality is
"The sum of a number and sixteen" translates to
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How would you write the equations: "I can spend no more than 
dollars when I go to the store today."
How would you write the equations: "I can spend no more than
The way the sentence is phrased suggests that the person can spend up to 
dollars but not a penny more. This suggests that 
, the amount spend can be 
but not exceed it.
So your answer is: 
The way the sentence is phrased suggests that the person can spend up to
So your answer is:
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Given the following problem, write the inequality.
Seven less than two times a number is greater than fourteen.
Given the following problem, write the inequality.
Seven less than two times a number is greater than fourteen.
Seven less than two times a number is greater than fourteen.
Let's look at the problem step by step.
If we do not know the value of a number, we give it a variable name. Let's say x. So, we see in the problem
Seven less than two times a number is greater than fourteen.
So, we will replace a number with x.
Seven less than two times x is greater than fourteen.
Now, we see that is says "two times" x, so we will write it like
Seven less than 2 x is greater than fourteen.
The problem says "seven less" than 2x. This simply means we are taking 2x and subtracting seven. So we get
2x - 7 is greater than fourteen
We know the symbol for "is greater than". We can write
2x - 7 > fourteen
Finally, we write out the number fourteen.
2x - 7 > 14
Seven less than two times a number is greater than fourteen.
Let's look at the problem step by step.
If we do not know the value of a number, we give it a variable name. Let's say x. So, we see in the problem
Seven less than two times a number is greater than fourteen.
So, we will replace a number with x.
Seven less than two times x is greater than fourteen.
Now, we see that is says "two times" x, so we will write it like
Seven less than 2 x is greater than fourteen.
The problem says "seven less" than 2x. This simply means we are taking 2x and subtracting seven. So we get
2x - 7 is greater than fourteen
We know the symbol for "is greater than". We can write
2x - 7 > fourteen
Finally, we write out the number fourteen.
2x - 7 > 14
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Express the following as an inequality:
Bob's amount of apples (
) is more than twice the amount of Adam's bananas (
).
Express the following as an inequality:
Bob's amount of apples (
To solve, you must convert the statement into an expression. The key work is "is". Whatever is on the left of that in the sentence will be on the left side of the expression. The same goes for the right. Thus, 
is on the left and 
is on the right.
To solve, you must convert the statement into an expression. The key work is "is". Whatever is on the left of that in the sentence will be on the left side of the expression. The same goes for the right. Thus,
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Write the following as a mathematical inequality:
A number is less than or equal to three times the sum of another number and five
Write the following as a mathematical inequality:
A number is less than or equal to three times the sum of another number and five
Write the following as a mathematical inequality:
A number is less than or equal to three times the sum of another number and five.
Let's begin with
"A number" let's call it x
"...is less than or equal to..."
So far we have:
Now,
"...three times..."
"...the sum of another number and five."
So, all together:
Write the following as a mathematical inequality:
A number is less than or equal to three times the sum of another number and five.
Let's begin with
"A number" let's call it x
"...is less than or equal to..."
So far we have:
Now,
"...three times..."
"...the sum of another number and five."
So, all together:
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Write the inequality:
Two less than twice a number is less than two.
Write the inequality:
Two less than twice a number is less than two.
Break up the statement by parts. Let that number be 
.
Twice a number: 
Two less than twice a number: 
Less than two: 
Combine the parts.
The answer is: 
Break up the statement by parts. Let that number be
Twice a number:
Two less than twice a number:
Less than two:
Combine the parts.
The answer is:
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Write the inequality: Three less than twice a number is more than three times the number.
Write the inequality: Three less than twice a number is more than three times the number.
Break up the sentence into parts. Let the number be 
.
Twice a number: 
Three less than twice a number: 
Three less than twice a number is more than: 
Three times the number: 
Combine the terms to form the inequality.
The answer is: 
Break up the sentence into parts. Let the number be
Twice a number:
Three less than twice a number:
Three less than twice a number is more than:
Three times the number:
Combine the terms to form the inequality.
The answer is:
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Write the inequality: A number less than three is less than three.
Write the inequality: A number less than three is less than three.
Let a number be 
. Split up the problem into parts.
A number less than three: 
Is less than three: 
Combine all the terms.
The answer is: 
Let a number be
A number less than three:
Is less than three:
Combine all the terms.
The answer is:
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Write the inequality: A number less than three is less than three.
Write the inequality: A number less than three is less than three.
Let a number be 
. Split up the problem into parts.
A number less than three: 
Is less than three: 
Combine all the terms.
The answer is: 
Let a number be
A number less than three:
Is less than three:
Combine all the terms.
The answer is:
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Write the inequality: Two more than three times a number is more than six.
Write the inequality: Two more than three times a number is more than six.
Split up the sentence into parts. Let the number be 
.
Two more than three times a number: 
More than six: 
Combine the parts to form an inequality.
The answer is: 
Split up the sentence into parts. Let the number be
Two more than three times a number:
More than six:
Combine the parts to form an inequality.
The answer is:
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Write the inequality: A number less than three is greater than five.
Write the inequality: A number less than three is greater than five.
Break up the terms and rewrite by parts.
A number less than three: 
Greater than five: 
Combine the terms.
The answer is: 
Break up the terms and rewrite by parts.
A number less than three:
Greater than five:
Combine the terms.
The answer is:
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Write the following inequality: Two less than three times a number is less than four.
Write the following inequality: Two less than three times a number is less than four.
Break up the statement into parts. Let 
be the number.
Three times a number: 
Two less than three times a number: 
Less than four: 
Combine the terms.
The answer is: 
Break up the statement into parts. Let
Three times a number:
Two less than three times a number:
Less than four:
Combine the terms.
The answer is:
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Write the inequality: Twice a number less than six is more than four.
Write the inequality: Twice a number less than six is more than four.
Break up the inequality into parts. Let a variable be the number.
Twice a number: 
Twice a number less than six: 
Is more than four: 
Combine the terms.
The answer is: 
Break up the inequality into parts. Let a variable be the number.
Twice a number:
Twice a number less than six:
Is more than four:
Combine the terms.
The answer is:
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Write the inequality: One less than twice the difference of five and twice a number is less than four.
Write the inequality: One less than twice the difference of five and twice a number is less than four.
In order to write this inequality, we need to break up the statement into parts.
Let the number be a random variable.
The difference of five and twice a number: 
Twice the difference of five and twice a number: 
One less than twice the difference of five and twice a number: 
Is less than four: 
Combine the terms.
The answer is: 
In order to write this inequality, we need to break up the statement into parts.
Let the number be a random variable.
The difference of five and twice a number:
Twice the difference of five and twice a number:
One less than twice the difference of five and twice a number:
Is less than four:
Combine the terms.
The answer is:
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Write the following inequality: Five times a number less than five is less than negative five.
Write the following inequality: Five times a number less than five is less than negative five.
Convert each part of the sentence into mathematical expressions. Let a random variable be the number.
Five times a number: 
Five times a number less than five: 
Is less than negative five: 
Combine the expressions.
The answer is: 
Convert each part of the sentence into mathematical expressions. Let a random variable be the number.
Five times a number:
Five times a number less than five:
Is less than negative five:
Combine the expressions.
The answer is:
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Write the inequality: Two less than eight times a number is at least seven.
Write the inequality: Two less than eight times a number is at least seven.
Let a number be 
. Break up the sentence to parts.
Eight times a number: 
Two less than eight times a number: 
Is at least seven: 
Combine the terms.
The answer is: 
Let a number be
Eight times a number:
Two less than eight times a number:
Is at least seven:
Combine the terms.
The answer is:
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Write the inequality: Eight more than two times a number is more than two.
Write the inequality: Eight more than two times a number is more than two.
Split the problem statement into parts.
Two times a number: 
Eight more than two times a number: 
Is more than two: 
Combine the terms to make an equation.
The answer is: 
Split the problem statement into parts.
Two times a number:
Eight more than two times a number:
Is more than two:
Combine the terms to make an equation.
The answer is:
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