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."
Table of Content
What are Inequalities?
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.
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