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.
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.
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