Question

How do you evaluate `5( 2x - 3) - 6x \leq 30`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each term in parenthesis by `color(red)(5)` to eliminate the parenthesis:

`color(red)(5)(2x - 3) - 6x <= 30`

`(color(red)(5) xx 2x) - (color(red)(5) xx 3) - 6x <= 30`

`10x - 15 - 6x <= 30`

Next, combine like terms on the left side of the inequality:

`10x - 6x - 15 <= 30`

`(10 - 6)x - 15 <= 30`

`4x - 15 <= 30`

Then, add `color(red)(15)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`4x - 15 + color(red)(15) <= 30 + color(red)(15)`

`4x - 0 <= 45`

`4x <= 45`

Now, divide each side of the inequality by `color(red)(4)` to solve for `x` while keeping the inequality balanced:

`(4x)/color(red)(4) <= 45/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) <= 45/4`

`x <= 45/4`