Question

How do you solve `16( x + 3) + 8( x + 2) < 64`?

Answer 1

See the entire solution process below:

Explanation:

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

`color(red)(16)(x + 3) + color(blue)(8)(x + 2) < 64`

`(color(red)(16) xx x) + (color(red)(16) xx 3) + (color(blue)(8) xx x) + (color(blue)(8) xx 2) < 64`

`16x + 48 + 8x + 16 < 64`

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

`16x + 8x + 48 + 16 < 64`

`(16 + 8)x + 64 < 64`

`24x + 64 < 64`

Then, subtract `color(red)(64)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`24x + 64 - color(red)(64) < 64 - color(red)(64)`

`24x + 0 < 0`

`24x < 0`

Now, divide each side of the inequality by `color(red)(24)` to solve for `x` while keeping the inequality balanced:

`(24x)/color(red)(24) < 0/color(red)(24)`

`(color(red)(cancel(color(black)(24)))x)/cancel(color(red)(24)) < 0`

`x < 0`