Question

How do you solve and graph `4.7-2.1x> - 7.9`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(4.7)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(red)(4.7) + 4.7 - 2.1x > -color(red)(4.7) - 7.9`

`0 - 2.1x > -12.6`

`-2.1x > -12.6`

Now, divide each side of the inequality by `color(blue)(-2.1)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative number we must reverse the inequality operator:

`(-2.1x)/color(blue)(-2.1) color(red)(<) (-12.6)/color(blue)(-2.1)`

`(color(blue)(cancel(color(black)(-2.1)))x)/cancel(color(blue)(-2.1)) color(red)(<) 6`

`x color(red)(<) 6`

The graphs for this is:

graph{x < 6 [-10, 10, -5, 5]}