SOLVING ONE STEP INEQUALITIES WORKSHEET

Problem 1 :

Solve for x :

5 + x  >  3 

Problem 2 :

Solve for p :  

p - 7  <  3

Problem 3 :

Solve for r :

2r  ≤  6

Problem 4 :

Solve for m :

(1/4)m  ≤  3

Problem 5 :

Solve for p :

8 - p  ≥  12

Problem 6 : 

Solve for m :  

m - 10  <  -15

Problem 7 :

Solve for v :  

v + 5/3  >  -1/3

Problem 8 :

Solve for m :

38 - m  ≤  -44

Problem 9 :

Solve for m :

-11m  >  22

Problem 10 :

Solve for v :

-25.7 - v  <  -40.3

Problem 11 :

When 7 is added to a number, we get the result greater than 25. Find the number. 

Problem 12 :

When we multiply a number by 4, we get the result less than 124. Find the number. 

Problem 13 :

When we divide a number by 7, we get the result greater than 14. Find the number. 

Problem 14 :

John had some candies. He gave 5 candies to his friend and now he has more than 18 candies. How many candies did John initially have ? 

Problem 15 :

Alex borrowed some money from Jose. After 3 years, Alex returned more than 2 times of borrowed money to Jose. If the returned money is $226, how much money did Alex borrow from Jose ?

Detailed Answer Key

Problem 1 :

Solve for x :

5 + x  >  3 

Solution : 

5 + x  >  3

Subtract 5 from each side. 

So, the value of x is greater than -2.

Problem 2 :

Solve for p :  

p - 7  <  3

Solution : 

p - 7  <  3

Add 7 to each side. 

So, the value of p is less than 10. 

Problem 3 :

Solve for r :

2r  ≤  6

Solution : 

2r  ≤  6

Divide each side by 2.

So, the value of r is less than or equal to 3. 

Problem 4 :

Solve for m :

(1/4)m  ≤  3

Solution : 

(1/4)m  ≤  3

Multiply each side by 4. 

So, the value of m is less than or equal to 12.

Problem 5 :

Solve for p :

8 - p  ≥  12

Solution : 

8 - p  ≥  12

In this problem, first we have to make p to be positive.

For that, we have to add p to each side. 

When we do so, we will have (12 + p) on the right side of the inequality.

Then, subtract 12 from each side to solve for p. 

or

p  ≤  -4

So, the value of p is less than or equal to -4.

Problem 6 : 

Solve for m :

m - 10  <  -15

Solution : 

m - 10  <  -15

Add 10 to each side. 

m  <  -5

So, the value of m is less than -5.

Problem 7 :

Solve for v :  

v + 5/3  >  -1/3

Solution : 

v + 5/3  >  -1/3

Subtract 5/3 from each side. 

v  >  -2

So, the value of v is greater than -2. 

Problem 8 :

Solve for m :

38 - m  ≤  -44

Solution : 

In this problem, first we have to make m to be positive.

For that, we have to add m to each side. 

When we do so, we will have (-44 + m) on the right side of the inequality.

Then, add 44 to each side to solve for m. 

82  ≤  m

m  ≥  82

So, the value of m is greater than 82.

Problem 9 :

Solve for m :

-11m  >  22

Solution : 

-11m  >  22

Divide each side by -11.

m  <  -2

So, the value of m is less than -2.

Problem 10 :

Solve for v :

-25.7 - v  <  -40.3

Solution : 

In this problem, first we have to make v to be positive.

For that, we have to add v to each side. 

When we do so, we will have (-40.3 + v) on the right side of the inequality.

Then, add 40.3 to each side to solve for v. 

14.6  <  v

v  >  14.6

So, the value of v is greater than 14.6.

Problem 11 :

When 7 is added to a number, we get the result greater than 25. Find the number. 

Solution : 

Let x be the required number. 

Given : When 7 is added to the number, the result is greater than 25.

Then, we have

x + 7  >  25

Subtract 7 from each side.

x  >  18

So, the required number is any number greater than 18.

Problem 12 :

When we multiply a number by 4, we get the result less than 124. Find the number. 

Solution : 

Let x be the required number. 

Given : When the number is multiplied by 4, the result is less than 125. 

Then, we have

4x  <  124

Divide each side by 4. 

x  <  31

So, the required number is any number less than 31.

Problem 13 :

When we divide a number by 7, we get the result greater than 14. Find the number. 

Solution : 

Let m be the required number. 

Given : When the number is divided by 7, the result is greater than 14. 

m / 7  >  14

Multiply each side by 7.

m  >  98

So, the required number is any number greater than 98.

Problem 14 :

John had some candies. He gave 5 candies to his friend and now he has more than 18 candies. How many candies did John initially have ? 

Solution : 

Let m be the no. of candies that John initially had. 

Given : After giving 5 candies to friend, John has more than 18 candies. 

Then, we have

m - 5   >  18

Add 5 to each side. 

m  >  23

So, John initially would have had more than 23 candies.

Problem 15 :

Alex borrowed some money from Jose. After 3 years, Alex returned more than 2 times of borrowed money to Jose. If the returned money is $226, how much money did Alex borrow from Jose ?

Solution : 

Let x be the borrowed money. 

Given : Alex returned more than 2 times of borrowed money to Jose. and the returned money is $226. 

Then, we have

226  >  2x

Divide each side by 2. 

113  >  x

x  <  113

So, the borrowed money is less than $113. 

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