Question

How do you graph the inequality `35x+25<6` on the coordinate plane?

Answer 1

See Below for Answer:

Explanation:

First, let's simplify the inequality. Pretend for a moment that the less than symbol `(<)` is an equal sign `(=)` for a moment. So we now have an equation such as:

`35x+25=6`

From there let's subtract `25` from both sides of the equation:

`25-25=0`

`6-25=-19`

Now we have a statment such as:

`35x=-19`

At this point, insert the less than symbol back in:

`35x<-19`

Now divide both sides by `35` to get `x` alone. The final answer should be:

`x<-19/35`

On a graph, it would look something like this:

graph{x<-19/35 [-10, 10, -5, 5]}

The one above is the simplified inequality version. Below is the unsimplified version.

Now, let's compare it to that of the unsimplified version:

graph{35x+26<6 [-10, 10, -5, 5]}

It's checks out! They are both equivalent. If you get a fraction, it's much easier to keep it in fraction form instead of converting it to decimal form (in this problem we faced `-19/25` as our fraction).

`x<-19/35` means that any value you substitute into that inequality of yours that is less than `-19/25` will work. Hence what is depicted on the graph. Any part of the shaded region will check out.