Question

How do you solve `1.2x + 8 < 9.6` and graph the solution graph the solution on a number line?

Answer 1

`x<1.333`

Explanation:

Move the `8` over so you have

`1.2x<1.6`

Then divide both sides by `1.2`. This will give you

`x < 1.6/1.2`

`x < 1.333...`

So in the end, you have `x<1.333` (notice that the sign doesn't change because there is no multiplication/division by a negative).

Then you would just put an arrow going left to negative infinity starting at `1.333` with an open circle. :)

Answer 2

See a solution process below:

Explanation:

First, subtract `color(red)(8)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`1.2x + 8 - color(red)(8) < 9.6 - color(red)(8)`

`1.2x + 0 < 1.6`

`1.2x < 1.6`

Next, divide each side of the inequality by `color(red)(1.2)` to solve for `x` while keeping the inequality balanced:

`(1.2x)/color(red)(1.2) < 1.6/color(red)(1.2)`

`(color(red)(cancel(color(black)(1.2)))x)/cancel(color(red)(1.2)) < 10/10 xx 1.6/color(red)(1.2)`

`x < 16/12`

`x < 4/3`

Or

`x < 1 1/3`

To graph this on the number line we need to put a hollow point at `1 1/3` on the number line because the inequality does not contain an "or equal to" clause. Therefore, `1 1/3` is not part of the solution set.

Then from that point we draw an arrow to the left because the inequality is a "less than" operator: