Question

How do you solve $3x + 16 = x$ ?

Answer 1

Hint:Rearrange the equation accordingly by addition, subtraction, division or multiplication. Then solve to get the value of x.

Complete step by step answer:
Subtract $x$ both the side
$ \Rightarrow 3x + 16 - x = x - x$
$ \Rightarrow 3x - x + 16 = 0$
$ \Rightarrow 2x + 16 = 0$
Subtract 16 both the side
$ \Rightarrow 2x + 16 - 16 = - 16$
$ \Rightarrow 2x + 0 = - 16$
$ \Rightarrow 2x = - 16$
Divide $2$ both the side
$ \Rightarrow 2x \div 2 = - 16 \div 2$
$ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{ - 16}}{2}$
$ \Rightarrow x = - 8$
Thus, $x = - 8$.

Additional information:
We can do the above solution by bringing the right-hand side $x$ to the left-hand side
$ \Rightarrow 3x + 16 - x = 0$
$ \Rightarrow 3x - x + 16 = 0$
$ \Rightarrow 2x + 16 = 0$
Now, take $ + 16$ to the right-hand side
$ \Rightarrow 2x = - 16$
The above equation can be written as
$ \Rightarrow \dfrac{{2x}}{1} = \dfrac{{ - 16}}{1}$
Cross multiply in such a way that on the left-hand side $x$ variable is present with no numeric value
$ \Rightarrow \dfrac{{x \times 1}}{1} = \dfrac{{ - 16}}{2}$
$ \Rightarrow x = - 8$
We can also check if the answer we got is correct or not by putting the value of $x = - 8$ in the given question or equation. The answer is correct when the left-hand side is equal to the right-hand side.
Let’s check if our answer $x = - 8$ is correct or not
Our question is $3x + 16 = x$
Here, left-hand side LHS is $3x + 16$ and right hand side RHS is $x$
Putting the value of $x$which is $x = - 8$ in LHS (left hand side)
$ \Rightarrow 3( - 8) + 16$
$ \Rightarrow - 24 + 16$
$ \Rightarrow - 8$
Now putting the value of $x$ which is $x = - 8$ in RHS(right hand side)
$ \Rightarrow - 8$
The values of LHS (left-hand side) and RHS (right-hand side) are the same.
$ \Rightarrow - 8 = - 8$
$LHS = RHS$

This implies our answer is correct which is $x = - 8$

Note: Positive and negative signs should be taken care of while solving the equations.
While checking the answer which is checking if the obtained value of $x$ is correct or not, LHS should always be equal to RHS. If LHS is not equal to RHS then the obtained value of $x$ is incorrect.