# Algebra 1 : How to solve absolute value equations

## Example Questions

### Example Question #31 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Let's first divide both sides by .

We have:

Subtract both sides by , we get .

Distribute the negative sign to get .

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

### Example Question #32 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Cross multiply and we get .

Then subtract both sides by  to get .

Let's divide both sides by  to make the math easier and then cross multiply.

We get .

Subtract both sides by  to get .

### Example Question #33 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Subtract both sides by , we get

Distribute the negative sign to get .

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

### Example Question #34 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Divide both sides by , we get .

Subtract both sides by , we get

Distribute the negative sign to get .

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

### Example Question #35 : How To Solve Absolute Value Equations

Solve for .

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

First subtract  to both sides.

Divide both sides by , we get .

Subtract both sides by , we get

Distribute the negative sign to get .

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

### Example Question #36 : How To Solve Absolute Value Equations

Solve for

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

Multiply both sides by , we get .

Subtract both sides by , we get

Distribute the negative sign to get .

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

### Example Question #37 : 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 second equation divide both sides by  to get .

Thus, our solutions for  are,

.

### Example Question #31 : 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

The two negatives become positive for the first equation.

For the second equation divide both sides by  to get .

Therefore, the solutions are

.

### Example Question #39 : 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 subtract  on both sides.

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

From here add  to both sides and divide both sides by , we get .

Therefore, the solutions are,

.

### Example Question #40 : 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 subtract  on both sides to get .

Remember since  is greater than  and is negative, our answer is negative. We treat as a subtraction problem.

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

From here add  to both sides and divide both sides by  to get .

Therefore, the solutions are,

.