**Inequality word problems :**

In this section, we will learn how to create an inequality for the given word problem by using algebraic reasoning and solve for the unknown quantity.

**Example 1 : **

Sum of a number and 5 is less than -12. Find the number.

**Solution :**

Let "x" be the number.

**Step 1 : **

Write the inequality.

x + 5 < -12

**Step 2 :**

Solve the inequality using Subtraction Property of Inequality.

Subtract 5 on from both sides.

(x + 5) - 5 < -12 - 5

x < -17

Hence, the number is any value less than -17.

**Example 2 : **

David has scored 110 points in the first level of a game. To play the third level, he needs more than 250 points. To play third level, how many points should he score in the second level ?

**Solution :**

Let "x" be points scored in the second level

**Step 1 : **

He has already had 110 points in the first level.

Points scored scored in the second level = x

Total points in the first two levels = x + 110

**Step 2 :**

Write the inequality.

To play third level, the total points in the first two levels should be more than 250. So, we have

x + 110 > 250

Subtract 110 on from both sides.

(x + 110) - 110 > 250 - 110

x > 140

Hence, he has to score more than 140 points in the second level.

**Example 3 : **

An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. If 5 freshmen are recruited, how many experienced men have to be recruited ?

**Solution :**

**Step 1 : **

Write the inequality.

x + y ≤ 9

**Step 2 :**

Plug y = 5.

x + 5 ≤ 9

Subtract 5 from both sides.

(x + 5) - 5 ≤ 9 - 5

x ≤ 4

To meet the given condition, no. of freshmen to be recruited can be less than or equal to 4.

**Example 4 : **

On the average, experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. How can this situation be expressed ?

**Solution :**

Let "x" and "y" be the number of experienced person and fresh workmen respectively.

**Step 1 : **

From the given information, we have

Total number of units of work done by experienced person per day = 5x.

Total number of units of work done by fresh one per day = 3y.

**Step 2 :**

Total number of units of work done by both experienced person and fresh one per day = 5x + 3y

As per the question, total number of units of work per day should be at least 30 units.

That is, total number of units of work (5x+3y) should be equal to 30 or more than 30.

So, we have 5x + 3y ≥ 30

After having gone through the stuff given above, we hope that the students would have understood "Inequality word problems".

Apart from the stuff given above, if you want to know more about "Inequality word problems", 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**