Question

Which of the following is a linear equation in one variable?
A. ${x^2} = 3$
B. $2x + 7 = 8$
C. $x > 0$
D. $x + y = 7$

Answer 1

Hint: We can define what are the conditions that must be satisfied for the equation to be a linear equation in one variable. Then we can check each of the options whether it satisfies the conditions or not. Then we can find the required equation by eliminating the wrong options.

Complete step-by-step answer:
We know that a linear equation in one variable is the equation which has degree one and has only one variable.
Now consider option A, ${x^2} = 3$.
As there is only one variable, we can say that it is an equation in one variable. But the power of the variable is 2. So, it is not a linear equation. Therefore, ${x^2} = 3$ is not a linear equation in one variable
Now consider option B, $2x + 7 = 8$.
As there is only one variable, we can say that it is an equation in one variable. But the power of the variable is also 1. So, it is a linear equation. As the 2 conditions satisfy, we can say that $2x + 7 = 8$ is a linear equation in one variable.
Now consider option C, $x > 0$
As there is no equal to sign, we can say that it is not an equation. So $x > 0$ is not a linear equation in one variable
Now consider option D, $x + y = 7$
We can see that there are 2 variables x and y. So, it is not an equation in one variable. So $x + y = 7$ is not a linear equation in one variable.
Therefore, the only linear equation in one variable is $2x + 7 = 8$
So, the correct answer is option B.

Note: Alternate method to solve this problem is given by,
We know that a linear equation in one variable is the equation which has degree one and has only one variable. We also know that the standard form of a linear equation in one variable is $ax + b = 0$
On checking the options, we can see that only the equation $2x + 7 = 8$ is in the form $ax + b = 0$.
Therefore, the only linear equation in one variable is $2x + 7 = 8$
So, the correct answer is option B.