Question

How do you solve `0.3( x + 1) \geq 0.2x - 0.3`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the left side of the inequality by multiplying each term within the parenthesis by `color(red)(0.3)`

`color(red)(0.3)(x + 1) >= 0.2x - 0.3`

`(color(red)(0.3) xx x) + (color(red)(0.3) xx 1) >= 0.2x - 0.3`

`0.3x + 0.3 >= 0.2x - 0.3`

Next, subtract `color(red)(0.3)` and `color(blue)(0.2x)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`0.3x + 0.3 - color(red)(0.3) - color(blue)(0.2x) >= 0.2x - 0.3 - color(red)(0.3) - color(blue)(0.2x)`

`0.3x - color(blue)(0.2x) + 0.3 - color(red)(0.3) >= 0.2x - color(blue)(0.2x) - 0.3 - color(red)(0.3)`

`0.1x + 0 >= 0 - 0.6`

`0.1x >= -0.6`

Now, divide each side of the inequality by `color(red)(0.1)` to solve for `x` while keeping the inequality balanced:

`(0.1x)/color(red)(0.1) >= -0.6/color(red)(0.1)`

`(color(red)(cancel(color(black)(0.1)))x)/cancel(color(red)(0.1)) >= -6`

`x >= -6`