Question

How do you solve `12-d> -8` and graph the solution on a number line?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(12)` from each side of the inequality to isolate the `d` term while keeping the inequality balanced:

`-color(red)(12) + 12 - d > -color(red)(12) - 8`

`0 - d > -20`

`-d > -20`

Now, multiply each side of the inequality by `color(blue)(-1)` to solve for `d` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we need to reverse the inequality operator:

`color(blue)(-1) xx -d color(red)(<) color(blue)(-1) xx -20`

`d color(red)(<) 20`

To graph this on the number line we draw a hollow circle on the number line at `20`.

The circle is hollow because the inequality operator does not contain and "or equal to" clause.

The we draw an arrow to the left of the circle because the inequality operator is a "less than" inequality: