Question

How do you solve `15x - 1= 2( 5x - 2) + 8`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`15x - 1 = color(red)(2)(5x - 2) + 8`

`15x - 1 = (color(red)(2) xx 5x) - (color(red)(2) xx 2) + 8`

`15x - 1 = 10x - 4 + 8`

`15x - 1 = 10x + 4`

Next, add `color(red)(1)` and subtract `color(blue)(10x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(blue)(10x) + 15x - 1 + color(red)(1) = -color(blue)(10x) + 10x + 4 + color(red)(1)`

`(-color(blue)(10) + 15)x - 0 = 0 + 5`

`5x = 5`

Now, divide each side of the equation by `color(red)(5)` to solve for `x` while keeping the equation balanced:

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

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 1`

`x = 1`