Question

How do you solve `3x+7=31`?

Answer 1

Subtract `7` from both sides and then divide both sides by `3` to get
`color(white)("XXXX")` `x=8`

Explanation:

With the exception of attempting to divide by zero, if you perform the same basic arithmetic operation (addition, subtraction, multiplication, division) to all terms on both sides of an equation using the same value, the equation remains valid.

So, given `3x+7=31`

We can subtract `7` from both sides
`color(white)("XXXX")` `3x+7-7 = 31-7`
`color(white)("XXXX")` `3x = 24`
and the new versions of equation are still valid.

Similarly, we can divide both sides of the last version by `3`
`color(white)("XXXX")` `x = 8`
isolating `x` on one side and a constant on the other
and the result is still valid (again).