Question

How do you solve $3x - 5 = 2x + 6$?

Answer 1

Hint: Since the equation given to us is a linear equation, we will rearrange the terms in the equation to get the value of $x$ which is the final answer. We shift all the variables to one side and constants to the other side. Later after doing some arithmetic operations we will get the desired answer.

Complete step-by-step solution:
We have the given equation as:
 $ \Rightarrow 3x - 5 = 2x + 6$
Now we will take the similar terms on the same side, on transferring $2x$ from the right-hand side to the left-hand side and transferring $ - 5$ from the left-hand side to the right-hand side, we get:
$ \Rightarrow 3x - 2x = 6 + 5$
On simplifying the left-hand side, we get:
 \[ \Rightarrow x = 6 + 5\]
On adding the right-hand side, we get:
$ \Rightarrow x = 11$

x =11 is the required solution.

Note: Now to check whether the answer is correct, we will substitute the value of $x = 11$ in the equation.
On substituting $x = 11$ in the left-hand side of the equation, we get:
$ \Rightarrow 2(11) + 6$
On simplifying we get:
$ \Rightarrow 22 + 6$ which is $28$, therefore the value of the left-hand side is $28$.
Now on substituting $x = 11$ in the right-hand side of the equation, we get:
 $ \Rightarrow 3(11) - 5$
On simplifying we get:
$ \Rightarrow 33 - 5$ Which is$28$, 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.
It is to be remembered that when a term which is addition or subtraction when transferred across the $ = $ sign, it becomes a term in subtraction and addition respectively.