Example

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

Solution

We start by removing parentheses:

After combining like terms, we have

Now we can add $7x$ to both sides:

Next we add $27$ to both sides:

Finally, divide both sides by $4$ (which does not reverse the inequality):

or

The solution set contains all numbers greater than or equal to $6$. In interval notation, this is

which has the following graph.