Example

Find the solution set. Write the solution set in interval notation and graph it on a number line.

Solution

Let's start by clearing fractions. To do so we multiply both sides by $7$, and multiply by a positive number does not reverse the inequality:

or

Now we subtract $42$ from both sides to get

Next we divide both sides by $-4$. This will reverse the inequality:

or

The solution set contains all numbers strictly greater than $35/2$. In interval notation, this is

which has the following graph.