Question

How do you solve `\frac{3x + 20+ 5x}{7} < - 4`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the inequality by `color(red)(7)` to eliminate the fraction while keeping the inequality balanced:

`color(red)(7) xx (3x + 20 + 5x)/7 < color(red)(7) xx -4`

`cancel(color(red)(7)) xx (3x + 20 + 5x)/color(red)(cancel(color(black)(7))) < -28`

`3x + 20 + 5x < -28`

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

`3x + 5x + 20 < -28`

`(3 + 5)x + 20 < -28`

`8x + 20 < -28`

Then, subtract `color(red)(20)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`8x + 20 - color(red)(20) < -28 - color(red)(20)`

`8x + 0 < -48`

`8x < -48`

Now, divide each side of the inequality by `color(red)(8)` to solve for `x` while keeping the inequality balanced:

`(8x)/color(red)(8) < -48/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) < -6`

`x < -6`