How can I solve the equation $8=5x+2$? The problem is $8=5x+2$
but I'm not sure how to solve it.
 A: $$ 8 = 5x + 2 $$
If we subtract two from both sides, this will not change the truth of the original equation. For example, since $3 = 3$, there is no harm in subtracting $2$ from both sides to get $1 = 1$. In order to 'get rid' of the $+2$, we can subtract $2$ from both sides:
$$ 8 - 2 = 5x + \color{blue}{2 - 2} $$
$$ 6 = 5x + \color{blue}{0} $$
$$ 6 = 5x $$
Now we have $6 = 5x$. We can divide both sides by $5$ to get:
$$ \frac65 = x $$
To summarize:


*

*You can add or subtract a number from both sides of an equation.

*You can multiply or divide any number, except $0$, on both sides of the equation.

The reason you can't divide or multiply by $0$ is that, informally speaking, you cannot divide by $0$. The answers here do a great job of explaining.

*

*You want to get the $x$ all by itself on one side.


A: Hint: What do we have to add to $2$ in order to get $8$? What do we have to multiply by $5$ to get the answer to my first question?
Alternative Approach/Spoiler Below:

 $$\begin{align}x &= 1\cdot x\\ &= \frac55\cdot x\\ &= \frac{5x}5\\ &= \frac{5x+0}5\\ &= \frac{5x+(2-2)}5\\ &= \frac{(5x+2)-2}5\\ &= \frac{8-2}5\\ &= \frac65.\end{align}$$

Another Approach/Spoiler Below:

 Multiply both sides by $\frac15$ (don't forget to distribute on the right-hand side) to get the equivalent equation $\frac85=x+\frac25$. Subtract $\frac25$ from both sides to get $\frac65=x$.

