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 $4x$ to both sides:

The variables have disappeared and we are left with a statement that is always false ( a contradiction). This means that the original inequality is always false. There are no solutions. The solution is the empty set, $\emptyset$. There is no interval or graph for the empty set.