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

May 12, 2017

See Below for Answer:

#### Explanation:

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

$35 x + 25 = 6$

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:

$35 x = - 19$

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

$35 x < - 19$

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

$x < - \frac{19}{35}$

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 $- \frac{19}{25}$ as our fraction).

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