Start by finding the roots of the equation by changing the inequality to an equal sign.

Now, make a number line with the two roots:

Pick a number less than and plug it into the inequality to see if it holds.

For ,

is clearly not true. The solution set cannot be .

Next, pick a number between .

For ,

is true so the solution set must include .

Finally, pick a number greater than .

For ,

is clearly not the so the solution set cannot be .

Thus, the solution set for this inequality is .

Add 26 on both sides.

Divide by two on both sides.

The answer is:

Subtract nine from both sides.

Divide by negative 3 on both sides. We will need to switch the sign.

The answer is:

Two numbers of like sign have a positive quotient.

Therefore, has as its solution set the set of points at which and are both positive or both negative.

To find this set of points, we identify the zeroes of both expressions.

Since is nonzero we have to exclude ; is excluded anyway since it would bring about a denominator of zero. We choose one test point on each of the three intervals and determine where the inequality is correct.

Choose :

- True.

Choose :

- False.

Choose :

- True.

The solution set is

Solving inequalities is very similar to solving an equation. We must start by isolating x by moving the terms farthest from it to the other side of the inequality. In this case, subtract 2from each side.

Now, divide both sides by 2.

First, we distribute the and then collect terms:

Now we solve for x, taking care to change the direction of the inequality if we divide by a negative number:

Add six on both sides.

Divide by three on both sides.

The answer is:

First, find the zeroes of the numerator and the denominator. This will give the boundary points of the intervals to be tested.

;

Since the numerator may be equal to 0, and are included as solutions. However, since the denominator may not be equal to 0, is excluded as a solution.

Now, test each of four intervals for inclusion in the solution set by substituting one test value from each:

Let's test :

This is false, so is excluded from the solution set.

Let's test :

This is true, so is included in the solution set.

Let's test :

This is false, so is excluded from the solution set.

Let's test :

This is true, so is included in the solution set.

The solution set is therefore .

The first thing we can do is clean up the right side of the equation by distributing the , and combining terms:

Now we can combine further. At some point, we'll have to divide by a negative number, which will change the direction of the inequality.

Add seven on both sides.

Divide by three on both sides.

The answer is: