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Encapsulate
math
LinEar EquationS in onE VariabLE

Linear equation in one variable can be expressed in the form of ax + b = 0, where ‘a’ and ‘b’
are rational numbers and ‘x’ is the variable.

Solving Equations
Solution of the Equation
The value of the variable that makes an equation
true, is known as the solution of the equation. Having variable on one side
• move constant to the constant side.
E.g., 2x – 3 = 9 ⇒ 2x = 9 + 3 = 12
reducing Equations • multiply/Divide both sides by the coefficients
of x.
to simple form E.g., 7x = 14 ⇒ 7x = 14 ⇒ x = 2
• eliminate the denominator by taking Lcm of 7 7
denominator and multiply both sides of equation Having variable on both sides
by the Lcm. • move constant to one side and variable to other
• solve the equation. side.
• verify the equation by putting the value of E.g., 3x – 4 = 2x + 3 ⇒ 3x – 2x = 3 + 4 ⇒ x = 7
unknown in equation. • Divide/multiply both sides by the coefficient
to linear form of x.
• solve by using cross-multiplication. E.g., 3x = 5x – 16 ⇒ 16 = 5x – 3x ⇒ 16 = 2x
• verify the equation by putting derived value of ⇒ 16 = 2x ⇒ x = 8
unknown variable. 2 2

Mental Maths
1. Is the solution of an equation always a natural number?
2. If three-fourths of a number minus 2 gives 1, what is the number?
3. Which method do you use when you move a term from one side of an equation to the other?
4. What will be the solution of the equation 4x + 9 = 1?
5. The sum of three consecutive odd numbers is 99. Which one of these three is a prime number?

49 Linear Equations in One Variable