Question

Linear equation in one variable has
(A) Only one variable with any power
(B) Only one term with a variable
(C) Only one variable with power $1$
(D) Only constant term

Answer 1

Hint:
Start with defining the linear equation in one variable. Consider each of the given options separately one by one. A linear equation in one variable is an equation consisting of only one variable with a power of $1$. Use this definition to eliminate incorrect options and find the correct answer.

Complete step by step solution:
Here in question, we are given four choices to complete a given statement “Linear equation in one variable has….”. Now we need to find the correct choices from the given four options.
In option (A) it is given “Only one variable with any power”. This means the linear equation in one variable has only one variable with any power. But this implies equations with one variable and power of $2,3,4{\text{ or 5}}$ which is not true since these equations are known as quadratic, cubic, or biquadratic. Hence, the option (A) cannot be the correct answer.
In option (B) it is given “Only one term with a variable”. This means the linear equation in one variable has only one term with a variable. This also implies that there can only be one term with a variable which is not true for a linear equation. Hence, the option (B) cannot be the correct answer.
In option (C) it is given “Only one variable with power one”. This means the linear equation in one variable has only one variable with a power one. Linear equations are those equations that are of the first order. If the equation has a homogeneous variable (i.e. only one variable), then this type of equation is known as a linear equation in one variable. Hence, the option (C) is the correct option.
In option (D) it is given “Only constant terms” which means the linear equation in one variable has only constant terms. This also implies that the equation with one variable term with power one and other constant is not a linear equation, which is not true for a linear equation.

Hence, we get the correct option (C) among the given four.

Note:
In a question like this, checking all the given choices is advisable to select the most appropriate option. An alternative approach can be taken by using the example equations according to the information given in each option. Use the examples to check whether it follows the definition of a linear equation or not.