A variable is a symbol (usually a letter) that is used to represent a number whose value can change or is not fixed.
Example: In the equation y = 2x + 3, the value of y changes when x changes. If x = 2, then y = 7.
Solved Examples
Example 1: Solve for x in the equation 3x + 5 = 17.
Solution:
3x + 5 = 17
⇒ 3x = 17 - 5
⇒ 3x = 12
⇒ x = 12/3
⇒ x = 4
Therefore, the value of "x" in the given equation is 4.
Example 2: Solve for "x" in the equation x2 − 4x + 3 = 0.
Solution:
x2 − 4x + 3 = 0
⇒ (x -3) (x - 1) = 0
Now, Let's set each factor equal to 0.
(x -3) = 0 ⇒ x = 3
⇒ (x - 1) = 0 ⇒ x = 1.
Example 3: Solve x in the equation 2/x = 3.
Solution:
2/x = 3
⇒ 2 = 3x
⇒ x = 2/3
Therefore, the value of x is 2/3.
Practice Questions
Q1. Evaluate the Expressions: If x = 3, find 4x + 2.
Q2. Evaluate the Expressions: If y = 5, find 3y - 4.
Q3. Evaluate the Expressions: If p = 7, find 2p + 5.
Q4. Evaluate the Expressions: If m = 4, find m2.
Q5. Evaluate the Expressions: If x = 2 and y = 3, find 3x + 2y.
