# College Algebra : Absolute Value Equations

## Example Questions

### Example Question #1 : Absolute Value Equations

Solve the following

There are no solutions

Explanation:

We have to set up two equations, which are.

Now lets solve for x in each equation.

So the solutions are  and

### Example Question #2 : Absolute Value Equations

Solve:

Explanation:

We need to set up two equations since we are dealing with absolute value

We solve for , in each equation to get the solutions.

### Example Question #1 : Absolute Value Equations

Solve:

Explanation:

We need to set up two equations since we are dealing with absolute value

We solve for , in each equation to get the solutions.

### Example Question #1 : Absolute Value Equations

Solve the following:

Explanation:

To solve, you must split the absolute value into the two following equations.

and

Now, solve for x and right it in interval form.

### Example Question #1 : Absolute Value Equations

Solve for x:

Explanation:

To solve  we need to find a way to reverse the operation of taking the absolute value. What we need to do is think about what the absolute value operation does to an expression. Since it makes everything positive, . So actually solving the original equation comes down to solving the following two equations:

So we get the two solutions as:

### Example Question #1 : Absolute Value Equations

Solve the following equation for .

Explanation:

We first need to get rid of the absolute value symbol to solve the equation. TO break this absolute value, we assign two values to the right hand side, as shown below.

We now proceed to solve each equation independently.

Starting with the first equation, we get

Now for the second equation,

### Example Question #1 : Absolute Value Equations

Explanation:

To simplify the radical, break the radical in the numerator down into its factors. When doing so, the radical in the bottom will call with one from the numerator.

### Example Question #1 : Absolute Value Equations

Solve the following equation:

Explanation:

To solve for  first isolate the absolute value portion on one side of the equation and all other constants on the other side.

Recall that the absolute value can come from either a negative or positive value therefore two possible equations are set up.

### Example Question #9 : Absolute Value Equations

Solve the equation: