Question

How do you solve `-7- 6( 1+ 6x ) < 275`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms within the parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`-7 - color(red)(6)(1 + 6x) < 275`

`-7 - (color(red)(6) xx 1) - (color(red)(6) xx 6x) < 275`

`-7 - 6 - 36x < 275`

`-13 - 36x < 275`

Now, add `color(red)(13)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`color(red)(13) - 13 - 36x < color(red)(13) + 275`

`0 - 36x < 288`

`-36x < 288`

Now, divide each side of the inequality by `color(blue)(-36)` to solve by `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-36x)/color(blue)(-36) color(red)(>) 288/color(blue)(-36)`

`(color(blue)(cancel(color(black)(-36)))x)/cancel(color(blue)(-36)) color(red)(>) -8`

`x > -8`