WRITING A VERBAL DESCRIPTION OF A TWO STEP INEQUALITY

In this section, you will learn how to write a verbal description to fit a two-step inequality.

Example 1 : 

Write a corresponding real-world problem to represent 2x + 20 ≤ 50.

Solution : 

Step 1 :

Analyze what each part of the inequality means mathematically.

x is the solution of the problem, the quantity you are looking for.

2x means that, for a reason given in the problem, the quantity you are looking for is multiplied by 2.

+ 20 means that, for a reason given in the problem, 20 is added to 2x.

≤ 20 means that after multiplying the solution x by 2 and adding to 20, the result can be no greater than 50.

Step 2 :

Think of some different situations in which a quantity x is multiplied by 2.

You run x miles per day for 2 days. So, 2x is the total distance run.

or

You buy 2 items each costing x dollars. So, 2x is the total cost.

Step 3 : 

Build on the situation and adjust it to create a verbal description that takes all of the information into account.

• Tomas has run 20 miles so far this week. If he intends to run 50 miles or less, how many miles on average should he run on each of the 2 days remaining in the week ?                                                 
• Manny buys 2 work shirts that are each the same price. After using a $20 gift card, he can spend no more than $50. What is the maximum amount he can spend on each shirt?

Example 2 : 

Write a corresponding real-world problem to represent 5x + 50 <  120.

Solution : 

Step 1 :

Analyze what each part of the inequality means mathematically.

x is the solution of the problem, the quantity you are looking for.

5x means that, for a reason given in the problem, the quantity you are looking for is multiplied by 5.

 + 50 means that, for a reason given in the problem, 50 is added to 5x.

 < 120 means that after multiplying the solution x by 5 nd adding to 50, the result can be greater than or equal to 120.

Step 2 :

Think of some different situations in which a quantity x is multiplied by 2.

You make x no. of cups of lemonade per minute for 5 minutes. So, 5x is the total no. of cups of lemonade.

or

You purchase 5 items each costing x dollars. So, 5x is the total cost.

Step 3 : 

Build on the situation and adjust it to create a verbal description that takes all of the information into account.

• A publisher ships a package of x number of books each weighing 5 pounds, plus a second package weighing 50 pounds. The total weight of both packages should be less than 120 pounds. Find the maximum number of books can be shipped.                                                     
• Leon is planning to buy a birthday gift of $50 to his friend and some number of candies where the cost of each candy is $5. The expense made by by Leon should be less than $120. Find the maximum number of candies that Leon can buy. 

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