Question

How do you solve `6> -5t-4` and graph the solution?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(4)` to each side of the inequality to isolate the `t` term while keeping the inequality balanced:

`6 + color(red)(4) > -5t - 4 + color(red)(4)`

`10 > -5t - 0`

`10 > -5t`

Now, divide each side of the inequality by `color(blue)(-5)` to solve for `t` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`10/color(blue)(-5) color(red)(<) (-5t)/color(blue)(-5)`

`-2 color(red)(<) (color(red)(cancel(color(black)(-5)))t)/cancel(color(blue)(-5))`

`-2 color(red)(<) t`

We can reverse or flip the entire inequality to state the solution in terms of `t`:

`t > -2`

To graph this we will draw a vertical line at `-2` on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the right side of the line because the inequality operator does contain a "greater than" clause:

graph{x > -2 [-10, 10, -5, 5]}