Question

How do you solve $3x = 16 - 5x$?

Answer 1

Hint: In this question, all one needs to do is bring similar terms to similar sides and then evaluate the value of the variable based on the final equation. Another approach will be to either add or subtract any term in such a way that one side is completely free of variables.

Complete step by step solution:
In this question, we use basic algebra and we will be discussing both the methods mentioned in the hint. Let’s start with the traditional method which is the second method of adding or subtracting variables first and then if needed, then constants too.
The equation we are working with is $3x = 16 - 5x$. In this equation, we can observe that if we add $5x$ to the right-hand side, then we can eliminate the variable on this side. But we can’t add anything to only one side as it will disbalance the equality. As such, we will have to add the same value to the left-hand side also. The new equation will be
$\
  3x + 5x = 16 - 5x + 5x \\
  8x = 16 \\
\ $
Thus, we can find out the value of x which is 2.
Moving on to the second approach, we simply move the variable on one side to the other side of equality. But remember, when you are doing this, the sign of the object being moved changes. Negative becomes positive and positive becomes negative. For example,
$\
  3 - 2 = 1 \\
  3 = 2 + 1 \\
\ $
In the equation below, we moved 2 from one side of equality to another and its sign changed. If we do not change the sign, the whole equality will be imbalanced and you will end up proving that $3 = - 1$ which is wrong.
Coming back to our original equation $3x = 16 - 5x$ we can see that moving $ - 5x$, in this case, will make one side fully variable while the other side fully constant which is the most optimal situation.
$\
  3x = 16 - 5x \\
  3x + 5x = 16 \\
  8x = 16 \\
  x = 2 \\
\ $

Here also we get the same answer which is x is equal to 2.

Note:
In the first approach, some may say that we want to subtract $3x$ as that will also leave one side free of variables and yes you can do it but observe that if you do it, the other side will still have constants as well as variables and so you will either need to add $8x$ to both sides or subtract 16 from both sides making the solution lengthy.