Question

How do you solve `6x - 3\leq 3( x - 1)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms on the right side of the inequality to eliminate the parenthesis:

`6x - 3 <= (3 xx x) - (3 xx 1)`

`6x - 3 <= 3x - 3`

Next, subtract `color(red)(3x)` and add `color(blue)(3)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`6x - 3 - color(red)(3x) + color(blue)(3) <= 3x - 3 - color(red)(3x) + color(blue)(3)`

`6x - color(red)(3x) - 3 + color(blue)(3) <= 3x - color(red)(3x) - 3 + color(blue)(3)`

`(6 - 3)x - 0 <= 0 - 0`

`3x <= 0`

Now, divide each side of the inequality by `color(red)(3)` to solve for `x` while keeping the inequality balanced:

`(3x)/color(red)(3) <= 0/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) <= 0`

`x <= 0`