Difference between equation and inequality
An equation is a mathematical expression which involves “=” symbol. The right hand side of the expression is equal to the left hand side of the expression.
The statements involving symbols like ‘<’(less than), ‘>’ (greater than), ‘\(\leq\)
Following example validates the difference between equation and inequality:
Statement 1: The distance between your house and school is exactly 4.5 kilometers,
The mathematical expression of the above statement is,
x = 4.5 km, where ‘x’ is the distance between house and the school.
Statement 2: The distance between your house and the school is at least 4.5 kilometers.
Here, the distance can be 4.5 km or more than that. Therefore the mathematical expression for the above statement is,
x \( \geq \)
Types of inequalities:
Numerical inequalities: If only numbers are involved in the expression, then it is a numerical inequality.
Example:\( 10 > 8, 5 < 7\)
Literal inequalities: x < 2, y > 5, z < 10 are the examples for literal inequalities.
Double inequalities: 5 < 7 < 9 read as 7 less than 9 and greater than 5 is an example for double inequality.
Strict inequality: Mathematical expressions involve only ‘<‘ or ‘>’ are called strict inequalities.
Example: \( 2x + 3 \leq 6, 2x + 3y \geq 6\)
Slack inequality: Mathematical expressions involve only \(‘\leq’\)
Example: \( 2x + 3 \leq 6, 2x + 3y \geq 6 \)
In the above examples, \( 2x + 3 < 6 \)
Similarly, \( 2x + 3y \geq 6 \)
Note: \( 4x^2 + 2x + 5 < 0 \)
Example: Classify the following expressions into
- Linear inequality in one variable.
- Linear inequality in two variables.
- Slack inequality.
\( 5x < 6, 8x + 3y \leq 5, 2x – 5 < 9 , 2x \leq 9 , 2x + 3y < 10 \)
|Linear inequality in one variable||Linear inequality in two variables||Slack inequality|
|5x < 6||8x + 3y ≥ 5||8x + 3y ≥ 5|
|2x – 5 < 9||2x + 3y < 10||2x ≤ 9|
|2x ≤ 9|
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