**Writing a verbal description of a two step inequality :**

In this section, we 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.

After having gone through the stuff given above, we hope that the students would have understood "Writing a verbal description of a two step inequality".

Apart from the stuff given above, if you want to know more about "Writing a verbal description of a two step inequality", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**