Two step inequality word problems worksheet with answers

Example 1 : 

Sum of two times of a number and 5 is less than -11. Find the number.

Solution :

Let x be the number.

Step 1 : 

Write the inequality.

2x + 5 < -11

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 5 on from both sides. 

(2x + 5) - 5 < -11 - 5

2x < -16

Divide both sides by 2

(2x) / 2 < (-16) / 2

x < -8

So, the number is any value less than -8. 

Example 2 : 

A mountain climbing team is camped at an altitude of 18,460 feet on Mount Everest. The team wants to reach more than 29,029-foot summit within 6 days. Find the average number of feet per day the team must climb to accomplish its objective.

Solution :

Let x be the average number of feet per day the team must climb to accomplish its objective. 

Step 1 : 

Write the inequality.

6x + 18460 ≥ 29029

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 18460 on from both sides. 

(6x + 18460) - 18460 ≥ 29029 - 18460

6x ≥ 10569

Divide both sides by 6

(6x) / 6 ≥ (10569) / 6

x ≥  1761.5

So, the team must climb at least 1761.5 feet per day to accomplish its objective.

Example 3 : 

The 45 members of the glee club are trying to raise more than $6,000, so they can compete in the state championship. They already have $1,230. Find the amount that each member must raise, on average, to meet the goal?

Solution :

Let x be the amount that each member must raise on average to meet the goal.  

Step 1 : 

Write the inequality.

45x + 1230 ≥ 6000

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 1230 on from both sides. 

(45x + 1230) - 1230 ≥ 6000 - 1230

45x ≥ 4770

Divide both sides by 45

(45x) / 45 ≥ (4770) / 45

x ≥ 106

So, each member must raise at least $106 on average to meet the goal

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Problem 1 : 

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

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 ?

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 ? 

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 ? 

Answers

Problem 1 : 

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

Answer :

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. 

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 ?

Answer :

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. 

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 ? 

Answer :

Step 1 : 

Write the inequality. 

x + y ≤ 9

Step 2 :

Substitute 5 for y.

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 ?

Answer :

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 is 

=  5x

Total number of units of work done by fresh one per day is

=  3y 

Step 2 :

Total number of units of work done by both experienced person and fresh one per day is

=  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.

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