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

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.