Question

How do you solve `3(x-18)=5(x-12)`?

Answer 1

`x=3`

Explanation:

`3(x-18)=5(x-12)`

Let's expand the equation by doing the multiplication
`3x-54=5x-60`

Now if we add to both sides `54`, this number will be moved from the left to the right
`color(red)(+54)+3x-54=5x-60color(red)(+54)`

`3x=5x-60+54`

Same thing can be applied with `5x`
`color(red)(-5x)+3x=5x-60+54color(red)(-5x)`

`3x-5x=-60+54`

And what we have to do now is just the sum of the similiar terms
`-2x=-6`

Multiplying both term by `-1`, we gain an equation with positive `x`
`color(blue)(-1)*-2x=-6*color(blue)(-1)`

`2x=6`

And to finally get the result we can divide both term by `2`
`2/\color(blue)(2)x=6/color(blue)(2)`

x=3

To check whether the result it's right, just plug in the value in the initial equation. If the left and right quantity are the same we did a good job.