Question

How do you solve and write the following in interval notation: `20x + 28 <=4( 4x + 5)`?

Answer 1

See a solution process below:

Explanation:

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

`20x + 28 <= color(red)(4)(4x + 5)`

`20x + 28 <= (color(red)(4) xx 4x) + (color(red)(4) xx 5)`

`20x + 28 <= 16x + 20`

Next, subtract `color(red)(28)` and `color(blue)(16x)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`20x - color(blue)(16x) + 28 - color(red)(28) <= 16x - color(blue)(16x) + 20 - color(red)(28)`

`(20 - color(blue)(16))x + 0 <= 0 - 8`

`4x <= -8`

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

`(4x)/color(red)(4) <= -8/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) <= -2`

`x <= -2`

Or, in interval notation:

`(-oo, -2]`