# SOLVING ONE STEP INEQUALITIES WORKSHEET

## About "Solving one step inequalities worksheet"

"Solving one step inequalities worksheet" is much useful to the parents and teachers who want to make their kids to practice solving one step inequalities.

Solving one step inequalities worksheet

## Solving one step inequalities - Examples

Problem 1 :

Solve : 5 + x  >  3

Solution :

Here 5 is added to the variable "x". To get rid of 5, we have to take "negative 5" on both sides and solve for "x" as explained below.

Hence, the vale of "x" is greater than "-2"

Let us look at the next example on "Solving one step inequalities worksheet"

Example 2 :

Solve :  p - 7  <  3

Solution :

Here 7 is subtracted from the variable "p". To get rid of "-7", we have to take "positive 7" on both sides and solve for "p" as explained below.

Hence, the vale of "p" is less than "10"

Let us look at the next example on "Solving one step inequalities worksheet"

Example 3 :

Solve :  2r    6

Solution :

Here "r" is multiplied by 2. To get rid of 2, we have to divide by 2 on both sides and solve for "r"  as explained below.

Hence, the vale of "r" is less than or equal to "3"

Let us look at the next example on "Solving one step inequalities worksheet"

Example 4 :

Solve :  (1/4)m    3

Solution :

Here "m" is divided by 4. To get rid of 4, we have to divide by 4 on both sides and solve for "m" as explained below.

Hence, the vale of "m" is less than or equal to "12"

Let us look at the next example on "Solving one step inequalities worksheet"

Example 5 :

Solve :  8 - p    12

Solution :

Here "p" is having negative sign.

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

For that, we have to add "p" on both sides. When we do so, we will have "12 + p" on the right side of the inequality.

Then, to get rid of "12" on the right side, we have to subtract 12 on both sides.

Therefore, we have to add "p" and subtract "12" on both sides and solve the inequality as explained below.

Hence, the vale of "p" is less than or equal to "-4"

## Solving one step inequalities worksheet - Practice problems

Problem 1 :

Solve :  m - 10  <  -15

Solution :

Here "10" is subtracted from "m". To get rid of 10, we have to add 10 on both sides and solve the inequality as explained below.

(m - 10) + 10  <  (-15) + 10

m  <  -5

Hence, the value of "m" is less than "-5

Let us look at the next problem on "Solving one step inequalities worksheet"

Problem 2 :

Solve :   v + 5 / 3  >  - 1/ 3

Solution :

Here "5/3" is added to "v". To get rid of 5/3, we have to subtract 5/3 on both sides and solve the inequality as explained below.

(v + 5/3) - 5/3  >  (-1/3) - 5/3

v  >  -2

Hence, the value of "v" is greater than "-2"

Let us look at the next problem on "Solving one step inequalities worksheet"

Problem 3 :

Solve :  38 - m    -44

Solution :

Here "m" is having negative sign.

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

For that, we have to add "m" on both sides. When we do so, we will have "- 44 + m" on the right side of the inequality.

Then, to get rid of "-44" on the right side, we have to add 44 on both sides.

Therefore, we have to add "m" and "44" on both sides and solve the inequality as explained below.

(38 - m) + m + 44    (-44) + m + 44

82    m

Hence, the value of "m" is greater than "82"

Let us look at the next problem on "Solving one step inequalities worksheet"

Problem 4 :

Solve :  -11m  >  22

Solution :

Here "m" is multiplied by "-11. To get rid of "-11", we have to divide by -11 on both sides.

In the given inequality, when we divide by negative number on both sides, we have to flip over ">" as "<".

-11m / -11  <  22 / (-11)

m  <  -2

Hence, the value of "m" is less than "-2"

Let us look at the next problem on "Solving one step inequalities worksheet"

Problem 5 :

Solve :  -25.7 - v  <  -40.3

Solution :

Here "v" is having negative sign.

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

For that, we have to add "m" on both sides. When we do so, we will have "- 40.3 + v" on the right side of the inequality.

Then, to get rid of "-40.3" on the right side, we have to add 40.3 on both sides.

Therefore, we have to add "v" and "40.3" on both sides and solve the inequality as explained below.

(-25.7 - v) + v + 40.3  <  (-40.3) + v + 40.3

14.6  <  v

Hence, the value of "v" is greater than "40.3"

## Solving one step inequalities - Word problems

Problem 1 :

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

Solution :

Let "x' be the required number.

According to the question, we have

x + 7  >  25

Here "7" is added to "x". To get rid of 7, we have to subtract 7 on both sides and solve the inequality as explained below.

(x + 7) - 7  >  (25) - 7

x  >  18

Hence, the required number is any number greater than "18".

Let us look at the next word problem on "Solving one step inequalities worksheet"

Problem 2 :

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

Solution :

Let "x' be the required number.

According to the question, we have

4x  <  124

Here "x" is multiplied by "4". To get rid of 4, we have to divide by 4 on both sides and solve the inequality as explained below.

4x / 4  <  124 / 4

x  <  31

Hence, the required number is any number less than "31".

Let us look at the next word problem on "Solving one step inequalities worksheet"

Problem 3 :

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

Solution :

Let "m' be the required number.

According to the question, we have

m / 7  >  14

Here "m" is divided by "7". To get rid of 7, we have to multiply by 7 on both sides and solve the inequality as explained below.

(m/7) x 7  >  14 x 7

m  >  98

Hence, the required number is any number greater than "98".

Let us look at the next word problem on "Solving one step inequalities worksheet"

Problem 4 :

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.

According to the question, we have

m - 5   >  18

Here "5" is subtracted from "m". To get rid of 5, we have to add 5 on both sides and solve the inequality as explained below.

(m - 5) + 5  >  18 + 5

m  >  23

Hence, John initially had more than 23 candies.

Let us look at the next word problem on "Solving one step inequalities worksheet"

Problem 5 :

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.

According to the question, we have

2x  <  226

Here "x" is multiplied by 2. To get rid of 2, we have to divide by 2 on both sides and solve the inequality as explained below.

2x / 2  <  226 / 2

x  <  113

Hence, the borrowed money is less than \$113.

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