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By the end of this section, you will be able to:
  • Solve applications with linear inequalities

Before you get started, take this readiness quiz.

  1. Write as an inequality: x is at least 30.
    If you missed this problem, review [link] .
  2. Solve 8 3 y < 41 .
    If you missed this problem, review [link] .

Solve applications with linear inequalities

Many real-life situations require us to solve inequalities. In fact, inequality applications are so common that we often do not even realize we are doing algebra. For example, how many gallons of gas can be put in the car for $20? Is the rent on an apartment affordable? Is there enough time before class to go get lunch, eat it, and return? How much money should each family member’s holiday gift cost without going over budget?

The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations. We will read the problem and make sure all the words are understood. Next, we will identify what we are looking for and assign a variable to represent it. We will restate the problem in one sentence to make it easy to translate into an inequality. Then, we will solve the inequality.

Emma got a new job and will have to move. Her monthly income will be $5,265. To qualify to rent an apartment, Emma’s monthly income must be at least three times as much as the rent. What is the highest rent Emma will qualify for?

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the highest rent Emma will qualify for Step 3. Name what we are looking for. Choose a variable to represent that quantity. Let r = the rent . Step 4. Translate into an inequality. First write a sentence that gives the information to find it. Emma’s monthly income must be at least three times the rent. Step 5. Solve the inequality. Remember, a > x has the same meaning as x < a . 5,625 3 r 1,755 r r 1,755 Step 6. Check the answer in the problem and make sure it makes sense. A maximum rent of $1,755 seems reasonable for an income of $5,625. Step 7. Answer the question with a complete sentence. The maximum rent is $1,755.

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Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet can safely support no more than 900 pounds. How many boxes can he safely load onto the pallet?

There can be no more than 20 boxes.

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The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people can safely ride the elevator?

A maximum of 14 people can safely ride in the elevator.

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Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. In that case, we must round the algebraic solution to a whole number. The context of the application will determine whether we round up or down. To check applications like this, we will round our answer to a number that is easy to compute with and make sure that number makes the inequality true.

Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost $254.12 each, including tax and delivery. What is the maximum number of tablets Dawn can buy?

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the maximum number of tablets Dawn can buy Step 3. Name what we are looking for. Choose a variable to represent that quantity. Let n = the number of tablets . Step 4. Translate . Write a sentence that gives the information to find it. Translate into an inequality . $254.12 times the number of tablets is no more than $4,000. 254.12 n 4,000 Step 5. Solve the inequality . n 15.74 But n must be a whole number of tablets, so round to 15. n 15 Step 6. Check the answer in the problem and make sure it makes sense. Rounding down the price to $250, 15 tablets would cost $3,750, while 16 tablets would be $4,000. So a maximum of 15 tablets at $254.12 seems reasonable. Step 7. Answer the question with a complete sentence. Dawn can buy a maximum of 15 tablets.

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Questions & Answers

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Ogenrwot
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They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
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Genetics is the study of heredity
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the study of living organisms and their interactions with one another and their environments
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the study of living organisms and their interactions with one another and their environment.
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what is the blood cells
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list any five characteristics of the blood cells
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lack electricity and its more savely than electronic microscope because its naturally by using of light
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advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
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is like gone fail us
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cells is the basic structure and functions of all living things
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What is classification
ISCONT Reply
is organisms that are similar into groups called tara
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in what situation (s) would be the use of a scanning electron microscope be ideal and why?
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A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
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what is cell divisoin?
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Diversity of living thing
ISCONT
what is cell division
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Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
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life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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