Table of Content

• What are Inequalities?
• Solving Inequalities with Addition and Subtraction
• Solving Inequalities with Addition and Subtraction
• Practice Questions on Solving Inequalities with Addition and Subtraction
• FAQs on Solving Inequalities with Addition and Subtraction

Inequality Name	Inequality Symbol
Greater than	>
Less than	<
Greater than Equal to	≥
Less than Equal to	≤

Solving Inequalities with Addition and Subtraction

To solve the inequalities, we add or subtract the same number according to the question from both sides of the inequality to simplify it. Find the additive inverse of the number added or subtracted in the given inequality and add it

Solving Inequalities with Addition

To solve the inequalities with the addition we add the same number on both sides of the inequality. Adding a number on both sides does not affect the inequality sign. The solving inequality with addition is mathematically represented as:

• p > q then, p + x > q + x
• p < q then, p + x < q + x
• p ≥ q then, p + x ≥ q + x
• p ≤ q then, p + x ≤ q + x

Solving Inequalities with Subtraction

To solve the inequalities with subtraction we subtract the same number on both sides of the inequality. Subtracting a number on both sides does not affect the inequality sign. Solving inequality with subtraction is mathematically represented as:

• p > q then, p – x > q – x
• p < q then, p – x < q – x
• p ≥ q then, p – x ≥ q – x
• p ≤ q then, p – x ≤ q – x

Solving Inequalities with Addition and Subtraction

Example 1: Solve x + 4 < 9

Solution:

x + 4 < 9

Subtracting 4 from both sides

x + 4 – 4 < 9 – 4

x < 5

Example 2: Evaluate y + 9 > 10

Solution:

y + 9 > 10

Subtracting 9 from both sides of inequality

y + 9 – 9 > 10 – 9

y > 1

Example 3: Solve the inequality p + 3 ≤ 16

Solution:

p + 3 ≤ 16

Subtracting 3 from both sides of inequality

p + 3 – 3 ≤ 16 – 3

p ≤ 13

Example 4: Solve q + 12 ≥ 23

Solution:

q + 12 ≥ 23

Subtracting 12 from both sides of inequality

q + 12 – 12 ≥ 23 – 12

q ≥ 11

Example 5: Solve z – 9 < 18

Solution:

z – 9 < 18

Adding 9 on both sides of inequality

z – 9 + 9 < 18 + 9

z < 27

Example 6: Evaluate w – 10 > 3

Solution:

w – 10 > 3

Adding 10 on both sides of inequality

w – 10 + 10 > 3 + 10

w > 13

Example 7: Solve the inequality c – 14 ≥ 5

Solution:

c – 14 ≥ 5

Adding 14 on both sides of inequality

c – 14 + 14 ≥ 5 + 14

c ≥ 19

Example 8: Solve d – 32 ≤ 15

Solution:

d – 32 ≤ 15

Adding 32 on both sides of inequality

d – 32 + 32 ≤ 15 + 32

d ≤ 47

Practice Questions on Solving Inequalities with Addition and Subtraction

Q1. Solve: b – 13 > 36

Q2. Evaluate: x + 8 < 17

Q3. Solve: a + 2 ≥ 15

Q4. Solve: z – 12 ≤ 25

Q5. Evaluate: y + 24 > 40

Q6. Solve the inequality: x – 10 < 17

FAQs on Solving Inequalities with Addition and Subtraction

What are Inequalities?

Inequalities are mathematical expressions that describe the relationship between two values, indicating that one value is either less than, greater than, less than or equal to, or greater than or equal to another value.

How to Solve Inequalities by Adding or Subtracting?

To solve the inequalities by adding or subtracting add or subtract the same number according to the question. The addition and subtraction in the inequality does not change the inequality.

What is Addition Property of Inequalities?

Addition property of inequalities are as follows:

• p > q then, p + x > q + x
• p < q then, p + x < q + x
• p ≥ q then, p + x ≥ q + x
• p ≤ q then, p + x ≤ q + x

What is Subtraction Property of Inequalities?

Subtraction property of inequalities are as follows:

• p > q then, p – x > q – x
• p < q then, p – x < q – x
• p ≥ q then, p – x ≥ q – x
• p ≤ q then, p – x ≤ q – x