Question

How do you solve $3x-7=x-9?$

Answer 1

Hint: The above question is a simple problem of linear equations in one variable. So, we will simply first understand the concept and definition of linear equations in one variable and then we will solve the above question to get the value of ‘x’. We will first shift all constant terms at the RHS and all the variable terms at the LHS. Then we will simplify the obtained equation by using the basic algebraic operations. Then we will get the value of x.

Complete step by step answer:
We know that the linear equation in one variable is an equation which has maximum one variable in the equation which is of order 1. Also, we know that a linear equation in one variable has only one solution.
And, also standard form of linear equation in one variable is represented as:
ax + b = 0 where a, b is a real number and a is not equal to zero.
So, we can say that $3x-7=x-9$ is a linear equation in one variable with variable x.
$\Rightarrow 3x-7=x-9$
Now, to solve $3x-7=x-9$ we will shift variables on one side of the equation from the other side of the equation and similarly, we will shift constant on the same side of the equation.
$\Rightarrow 3x-7=x-9$
$\Rightarrow 3x-x=7-9$
$\Rightarrow 2x=-2$
So, after dividing both side by 2 we will get:
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{2x}{2}}={\displaystyle \frac{-2}{2}}\\ & \Rightarrow x=-1\end{array}$$
Now, when we put $$x=-1$$ in the equation given above, then we will get $-10=-10$ , which satisfies the equality.
Hence, $$x=-1$$ is our required answer.

Note:
Students are required to recall the linear equations and basic properties of linear equations to solve these types of questions. We can verify the answer by putting the value in the given equation. On solving the equation if we get the values of LHS and RHS equal it means that the answer is correct. Students are also required to note that when we shift a variable or constant from one side of the equation to the other side of the equation then the sign of the variable gets reversed and magnitude remains the same.