S.2 MATHEMATICS LESSON : LINEAR INEQUALITIES

⁣Linear inequalities are mathematical expressions that compare two quantities using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). These inequalities involve linear functions, meaning every term in the inequality has a degree of 1.

For example, consider the linear inequality 2x + 3 < 7. This inequality states that the expression 2x + 3 is less than 7. To solve this inequality, we can follow these steps:

1. Subtract 3 from both sides: 2x + 3 - 3 < 7 - 3
Simplified: 2x < 4

2. Divide both sides by 2: (2x) / 2 < 4 / 2
Simplified: x < 2

Therefore, the solution to the linear inequality 2x + 3 < 7 is x < 2. This means that any value of x less than 2 would satisfy the inequality.

Linear inequalities can also involve variables on both sides of the inequality symbol. For example, consider the linear inequality 3x - 2 ≥ 5x + 1. To solve this inequality, we can follow similar steps:

1. Subtract 5x from both sides: 3x - 2 - 5x ≥ 5x + 1 - 5x
Simplified: -2x - 2 ≥ 1

2. Add 2 to both sides: -2x - 2 + 2 ≥ 1 + 2
Simplified: -2x ≥ 3

3. Divide both sides by -2 and reverse the inequality symbol: (-2x) / -2 ≤ 3 / -2
Simplified: x ≤ -3/2

Therefore, the solution to the linear inequality 3x - 2 ≥ 5x + 1 is x ≤ -3/2. This means that any value of x less than or equal to -3/2 would satisfy the inequality.