First, combine the x's on the left side: .

Then, move all the x's to the left side: , which simplifies to .

Next, move all other numbers to the right side: , which simplifies to . 

Lastly, we divide the entire problem by -1, and this flips the inequality sign.

This gives us .

Now we take the square root of both sides to get our final answer: 

First distribute the -4 to give:

Subtract x from both sides to get x on one side to give:

Subtract 8 from both sides to get x term by itself to give:

Divide both sides by -9, and remember when dividing or multiplying both sides by a negative it changes the inequality to give:

Simplify fraction to give final answer:

Write the inequality in parts before simplifying.

A number squared:  

Two less than a number squared:  

Two times the quantity of two less than a number squared:  

Is less than four:  

Divide by two on both sides.

Simplify both sides.

Add two on both sides.

Simplify both sides.

Square root both sides.

This will split into two solutions.

The first answer is:  

There will be a negative component as well for the second answer.

Dividing by a negative one on both sides will result in switching the sign.

The answers are:  

 Can be written as a compound inequality statement:

 or 

Solving these inequalities gives: 

1. Rewrite as a compound inequality statement:

 or 

2. Simplify:

  becomes 

 becomes 

Add 4 to both sides.

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

Split the inequality into two possible cases as follows, based on the absolute values.

First case:

Second case: 

Let's find the inequality of the first case.

Multiply both sides by x + 6.

Subtract x from both sides, then subtract 3 from both sides.

Divide both sides by 3.

Let's find the inequality of the second case.

Multiply both sides by x + 6.

Simplify.

Add x to both sides, then subtract 3 from both sides.

Divide both sides by 5.

So the range of x-values is   and  .

For a compound inequality, we solve each inequality individually. Thus, for the first inequality, , we obtain the solution  and for the second inequality, , we obtain the solution . In interval notation, the solutions are  and , respectively. Because our compound inequality has the word "or", this means we union the two solutions to obatin . 

or, in interval notation, 

Let  be Sam's age, and let  be his brother's age.

In the problem, we are told that the sum of their ages is at least 18. Represent this with an inequality:

Sam's age is three years more than twice his brothers age. Write this mathematically as:

Plug in for the value in the inequality and solve for :

The age of Sam's brother is less than or equal to  years.