Question

How do you solve and graph `-2b + 4 > -6`?

Answer 1

See a solution process below:

Explanation:

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

`-2b + 4 - color(red)(4) > -6 - color(red)(4)`

`-2b + 0 > -10`

`-2b > -10`

Now, divide each side of the inequality by `color(blue)(-2)` to solve for `b`. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-2b)/color(blue)(-2) color(red)(<) (-10)/color(blue)(-2)`

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

`b < 5`

To graph this inequality we will draw a vertical line at `5` on the horizontal axis.

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

We will shade to the left of the dashed line because the inequality operator contains a "less than" operator:

graph{x < 5}