# Algebra 1 : How to solve absolute value equations

## Example Questions

### Example Question #41 : How To Solve Absolute Value Equations

Solve for .

Explanation:

To solve this problem we first need to isolate the variable on one side with all other constants on the other side.

To accomplish this perform the opposite opperation therefore subtract  on both sides.

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will set up two equations to solve,

and .

For the second equation divide both sides by  to get .

Therefore the solutions are,

.

### Example Question #42 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

and .

For the first equation add  to both sides to get .

For the second equation, by distributing the negative sign, we have:

Now subtract  to both sides and divide both sides by  to get .

Therefore, the solutions are,

.

### Example Question #43 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

Equation 1:

Add  to both sides.

Equation 2:

By distributing the negative sign, we have:  Subtract  to both sides and divide both sides by , we get . Remember, since  is greater than  and is negative, our answer is negative and we treat as a normal subtraction problem.

Therefore, the solutions are,

.

### Example Question #44 : How To Solve Absolute Value Equations

Solve for .

Explanation:

First we will need to isolate the variable on one side of the equation and all other constants on the other side.

Divide both sides by .

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

Equation 2:

Divide  on both sides to get .

Therefore, the solutions are,

.

### Example Question #45 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

Divide  on both sides. .

Equation 2:

Divide  on both sides. .

Therefore, the solutions are,

.

### Example Question #41 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

Subtract  to both sides. Then divide  to both sides.

Equation 2:

By distributing the negative sign, we have:

Add  to both sides and divide both sides by , we get .

Therefore, the solutions are,

.

### Example Question #47 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

Multiply  on both sides. .

Equation 2:

Multiply  on both sides and divide  on both sides. .

Therefore, the solutions are, .

### Example Question #48 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation1:

Subtract  on both sides and then multiply  on both sides to get

Equation2:

By distributing the negative sign, we have: . Add  to both sides and multiply both sides by , we get .

Therefore, the solutions are,

.

Solve.

No solution

Explanation:

### Example Question #50 : How To Solve Absolute Value Equations

Solve for :

or

or

or

Explanation:

We define the absolute value of a number as that number's distance from  on the number line. Given , we therefore must solve for two possibilities:

1.) , or

2.)

Solving #1, we get:

Solving #2, we get:

Consequently, the solution is  or .