Linear Equations in One Variable
An equation of the type ax + b = 0, where a ≠ 0, is called a linear equation in the variable x.
Solution or root:
Any value (or values) of the variable (or variables) which when substituted in an equation
makes both its sides equal, is called a solution (or root) of the equation.
Solving an equation:
To solve an equation is to find all its solutions (or roots), and the process of finding all the
solutions is called solving the equation.
Solving linear equations in one variable:
● Simplify both sides by removing brackets and collecting like terms
● Remove fractions (or decimals) by multiplying both sides by an appropriate number
(LCM of denominators or a power of 10 in case of decimals).
● Isolate all variable terms on one side and all constants on the other side.
● Make the coefficient of the variable 1.
MCQs
1. If 𝑥 + 3𝑦 = 5. Then the value of a and b for which the equation is a
Linear equation in one variable x
I. a = 4 and b =2
II. a = 3 and b =2
III. a = 2 and b =4
IV. none of these
2. In the equation 3x = 4-x, transposing -x to LHS we get
I. 3x - x = 4
II. 3x + x = 4
III. -3x + x = 4
IV. -3x - x = 4
3. If x/3 + 1 = 7/15, then which of the following is correct?
I. x/3 = 7/15 - 1
II. x/3 = -7/15 + 1
III. x/3 = -7/15 - 1
IV. none of these
4. If 7x+15 = 50, then which of the following is the solution of the equation?
I. -5
II. 65/7
III. 5
IV. 1/5
