Question

How do you solve `6(x+4)=8(x-2)`?

Answer 1

`6(x+4) = 8(x-2)`
`6x+24 = 8x - 16`
`40 = 2x`
`20 = x`

Explanation:

To solve this equation, we first must expand both sets of brackets. To do this, multiply the number or letter on the outside of the brackets by the numbers or letter on the inside.

We'll start with the left side of the equals sign.

`6(x+4)`
`6x + 24`

`6` multiplied by `x` gives `6x`
`6` multiplied by `4` gives `24`

So the sum currently looks like this:

`6x + 24 = 8(x+2)`

Now we must expand the brackets on the right side of the equals sign.

`8(x-2)`
`8x - 16`

`8` multiplied by `x` gives `8x`
`8` multiplied by `-2` gives `-16`

So now the sum looks a little more approachable, like this:

`6x + 24 = 8x - 16`

To finish the sum, we have to have the like terms on the same side of the equal sign. In other words, we have to get the `x`'s on one side of the equals sign and the numbers on the other.

First, we have to cancel out the `-16` by adding `16` to both sides of the equals sign.

This gives `6x + 40 = 8x`

Then, cancel out the `6x` by taking `6x` off both sides of the equals sign.

This gives `40 = 2x`

Finally, to fully simplify the answer, divide both sides of the equals sign by two to get a single `x`

Giving: `20 = x`

Hope this helped!