Question

How do you solve for $x$ : $2x - 3 = 5x + 12$ ?

Answer 1

Hint: In this question, we are given an equation in terms of $x$ , and we have been asked to solve it. Since the given equation is a linear equation in one variable, you can just simply shift the terms to the other side such that all the constants are on one side and all the variable terms on the other side. Just simplify after this and finally we will get your required answer.

Complete step-by-step solution:
We are given a linear equation in one variable and we have to solve it, that is, we have to find the value of $x$ .
$ \Rightarrow 2x - 3 = 5x + 12$ …. (given)
We will shift the terms such that the constants are on the right-hand side and the variables are on the left-hand side. While shifting, take care of the positive and negative signs.
$ \Rightarrow 2x - 5x = 12 + 3$
Now, add the terms on the right-hand side and subtract on the left-hand side.
$ \Rightarrow - 3x = 15$
Shift the coefficient of the variable to the other side and divide.
$ \Rightarrow x = \dfrac{{15}}{{ - 3}} = - 5$

Hence, we get $x = - 5$.

Note: Now, we can check whether the answer that we have found is correct or not. Simply, put the value of $x$ in the given equation and if you get LHS = RHS, then our answer is correct.
We are given the following equation,
$ \Rightarrow 2x - 3 = 5x + 12$
Putting $x = - 5$ in the given equation,
$ \Rightarrow 2\left( { - 5} \right) - 3 = 5\left( { - 5} \right) + 12$
$ \Rightarrow - 10 - 3 = - 25 + 12$
Solving both the sides, we get,
$ \Rightarrow - 13 = - 13$
Since the left-hand side is equal to the right-hand side, we can say that the value that we have found is correct.
Hence, in this way, you can check your answer.