Question

How do you solve $3x - 15 = x + 21$?

Answer 1

Hint: In this question the equation given to us is a linear equation, we will rearrange the terms in the equation to get the value of $x$. On doing some simplification we get the required answer.

Complete step-by-step solution:
We have the given equation as:
$3x - 15 = x + 21$
Now we will take the similar terms on the same side, on transferring $x$ from the right-hand side to the left-hand side and transferring $15$ from the left-hand side to the right-hand side, we get:
$\Rightarrow$$3x - x = 15 + 21$
On simplifying the left-hand side, we get:
$\Rightarrow$$2x = 15 + 21$
On simplifying the right-hand side, we get:
$\Rightarrow$$2x = 36$
Now on transferring $2$ from the left-hand side to the right-hand side we get:
$\Rightarrow$$x = \dfrac{{36}}{2}$
On simplifying the fraction, we get:
$\Rightarrow$$x = 18$

The value of x is equal to 18.

Note: Now to check whether the answer is correct, we will substitute the value of $x = 18$ in the equation.
On substituting $x = 18$ in the left-hand side of the equation, we get:
$ \Rightarrow 3(18) - 15$
On simplifying we get:
$ \Rightarrow 54 - 15$which is $39$, therefore the value of the left-hand side is $39$.
Now on substituting $x = 18$ in the right-hand side of the equation, we get:
$ \Rightarrow 18 + 21$
On simplifying we get:
$ \Rightarrow 39$, since the value of the left-hand side is equal to the value of the right-hand side, the answer is correct
It is to be remembered that the equation given above is a linear equation which has only one variable which is $x$.
When there is one variable in an equation, we can find its solution by addition or subtraction, when there are two or more than two variables in the equation, we need that many equations to solve the question. The solution can be found using elimination method or by using a matrix.