Question

What is 5(x+17)=100?

Answer 1

`x = 3`

Explanation:

`5 (x + 17) = 100`

`5x + 85 = 100`

(*`5 xx 17 = 85`)

Using algebraic manipulation:

`5x = 100 - 85`

`5x = 15`

`x = 15/5`

`x = 3`

Answer 2

`x=3`

Explanation:

Given: `5(x+17)=100`

`color(blue)("Approach 1 - shows usfull methods")`

Multiply everything inside the brackets by the 5 that is outside

`5x+85=100`

To 'get rid' of the 85 on the left subtract `color(red)(85)` from BOTH sides

`color(green)(5x+ubrace(85color(red)(-85))=100color(red)(-85))`
`color(white)("dddddd")darr`
`color(green)(5x+color(white)("d.d")0color(white)("d.d")=color(white)("dd")15)`

To get rid of the `5` from `5x` divide both sides by `color(red)(5)`

`color(green)(5/color(red)(5) xcolor(white)("d")=color(white)("d")15/color(red)(5)`

But `5/5=1 and 1xx x = x` and `15/5=3` giving:

`color(green)(x=3)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Approach 2 - quicker as it uses less steps")`

`5(x+17)=100`

Divide both sides by 5

`x+17=20`

Subtract 17 from both sides

`x=3`