**Inequality word problems worksheet :**

Worksheet on inequality word problems is much useful to the students who would like to practice solving real world problems involving inequalities.

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

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 ?

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 ?

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 ?

**Problem 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.

**Problem 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.

**Problem 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.

**Problem 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 worksheet".

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