WRITING AND SOLVING ONE STEP INEQUALITIES 

In this section, you 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

So, 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

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

Example 3 : 

An employer recruits experienced and fresh workmen 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 :

Let x be the no. of freshmen to be recruited. 

Step 1 : 

Write the inequality. 

x + 5 ≤ 9

Step 2 :

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 : 

An employee of a factory has to maintain an output of at least 30 units of work per week. If there are five working day in a week, how many units of work to be done by him per day ? 

Solution :

Let x be the no. of units of work done per day. 

Step 1 : 

From the given information, we have

Total number of units of work done per week  =  5x

Step 2 :

Write the inequality. 

As per the question, total number of units of work done per week should be at least 30 units. So, we have

5x ≥ 30

Divide both sides by 5

5x/5 ≥ 30/5

x ≥ 6

So, the number of units of work to be done per day should be at least 6.

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