Question

How do you solve for y in the equation $x = y + 5$?

Answer 1

To solve the equation, $x = y + 5$, we will first learn how to solve such equations, then we will learn what does solving for y imply, after that, we will use certain examples to show how to operate with different algebraic expressions to simplify our answer. To solve for y, we will subtract both sides by 5 and then simplify to get our answer.

Complete step by step answer:
We are given an equation, $x = y + 5$, we are asked to solve for y. Solve for y, means we have to simplify the terms in such a way that we can rewrite the equation for y.
To simplify such equations, we will use algebraic operations like addition, subtraction, multiplication, and division.
If we have, $3x + 2y = 8$, then we will first move the terms containing x to the left side, after that, we can take 2 from that side, as we are asked to solve for y.
$\Rightarrow 3x + 2y - 3x = 8 - 3x$
Simplify the terms,
$\Rightarrow 2y = 8 - 3x$
Divide both sides by 2,
$\Rightarrow y = \dfrac{8}{2} - \dfrac{{3x}}{2}$
Cancel out the common factors,
$\Rightarrow y = 4 - \dfrac{{3x}}{2}$
Now, we are given in our question, the equation, $x = y + 5$.
We have 5 along with y, so we can subtract 5 on both sides to cancel that term. So, we get,
$\Rightarrow x - 5 = y + 5 - 5$
Simplify the terms,
$\Rightarrow y = x - 5$

Note: While solving such questions, always remember that variables are added to only variables of their kind. For example,
We know that $3x + 2x = 5x$, but we cannot $3x$ and $2y$ like, $3x + 2y = 5xy$ or add 8 and $2x$ like $8 + 2x = 10x$ as doing these are incorrect steps. Only like terms can be added or subtracted together. Also, remember that we cannot add ${x^2}$ and $x$ or any such higher power and lower powers.