Solving Linear Equations and Inequalities

Solving Linear Equations and Inequalities

 

Task Background: Equations and inequalities are very useful in the real world. For example, you may need to buy various items, such as milk and oranges, at the grocery store. If milk costs $3, and oranges cost $0.10 each, you could come up with an equation that gives the total price of $5. Then, you could use a variable (x = oranges) to represent the number of oranges bought. If you know that you have exactly $5 to spend, then an equation could be created:

 

Cost of milk + (cost per orange × number of oranges) = $5

 

or

<align=center>$3 + 0.10x = $5

 

This equation simply gives you the option to substitute various values of the number of oranges bought for x to ensure that you spend exactly $5.

 

An inequality, on the other hand, may state that you do not want to spend exactly $5 but that you want to stay below $5. Therefore, this inequality would be created as follows:

 

$3 + 0.10x < $5

 

This states that you want to spend less than $5 for the milk and oranges.

 

When you enter the workplace, you will encounter numerous equations and inequalities that will need to be analyzed and calculated with great accuracy. The importance is to first understand the differences between equations and inequalities and how to solve them.

 

Primary Task Response

 

Scenario: You have just graduated from college, and you have started your first big project at your new job. Your boss informs you that you are responsible for the Equations and Inequalities section of the project and for presenting your ideas to the team. Prepare for the meeting by discussing the following:

 

Part I: Provide a 1-variable linear equation of your own creation. (If you are struggling with coming up with an example, feel free to find one in your textbook.) Explain the techniques, and show the steps used for solving the equation. Check that your solution is correct.

 

Part II: Using the same 1-variable linear equation that you created in Part I, change the linear equation to a linear inequality (Use either < or >). Explain the techniques, and show the steps used for manipulating the linear inequality. Check that your solution is correct.

 

Part III: In 1 paragraph, summarize your results by discussing the following:

 

  • Interpret the solution to the linear equation and inequality, and explain the differences in your results. Explain how you know if a value is a solution for the inequality.

 

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