Solve Inequalities with Addition and Subtraction

The addition and subtraction rule for inequalities states that inequality still holds when the same number is added or subtracted from both sides of the inequality.

In this article, we will explore solving inequalities with addition and subtraction along with solving inequalities with addition and solving inequalities with subtraction. We will also solve some examples related to it. Let’s start our learning on the topic “Solve Inequalities with Addition and Subtraction.”

The inequalities are expressions with inequality symbols that relate two unequal values or expressions. Some examples of inequalities are 2 < 7, x ≥ 10 etc. Inequalities are useful to compare the quantities that are not equal.

Different Inequalities Symbols

The below table represents the different inequality symbols.

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

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

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

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