Question

How do you solve `5( 2x + 1) = 3( 5x - 4)`?

Answer 1

`x = 17/5`

Explanation:

First, on each side of the equation expand the terms within parenthesis:

`(color(red)(5) * 2x) + (color(red)(5) * 1) = (color(blue)(3) * 5x) - (color(blue)(3) * 4)`

`10x + 5 = 15x - 12`

Next, we can isolate the `x` terms on the right side of the equation and the constants on the left side of the equation while keeping the equation balanced:

`10x + 5 - color(red)(10x + 12) = 15x - 12 - color(red)(10x + 12)`

`10x - color(red)(10x) + 5 + color(red)(12) = 15x - color(red)(10x) - 12 + color(red)(12)`

`0 + 5 + 12 = (15 - 10)x - 0`

`17 = 5x`

Now we can solve for `x` while keeping the equation balanced:

`17/color(red)(5) = (5x)/color(red)(5)`

`17/5 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`17/5 = x`

`x = 17/5`

Answer 2

Work away the brackets first:

Explanation:

`->5*2x+5*1=3*5x-3*4`
`->10x+5=15x-12`

Take the `x`'s and numbers to different sides os the `=`by adding `12` and subtracting `10x`:
`->cancel(10x)-cancel(10x)+5+12=15x-10x-cancel12+cancel12`
`->17=5x->x=17/5=3 2/5`