When dealing with absolute value equations, we need to deal with negative values as well.

 Subtract  on both sides.

 Distribute the negative sign to each term in the parenthesEs.

 Add  on both sides.

 Divide both sides by .

Answers are 

When dealing with absolute value equations, we need to deal with negative values as well.

 Add  on both sides.

 Subtract  on both sides.

 Distribute the negative sign to each term in the parentheses.

 Add   on both sides.

 Divide  on both sides.

Answers are 

To solve absolute value equations, first we must isolate the absolute value:

Now that the absolute value is the only thing on the left hand side of the equation, we can solve for x.

Keep in mind that the absolute value makes whatever is inside of it a positive value. This means that and are both valid in solving the equation.

Setting both of these equal to 3 and solving for x, we get

As a check, plug each of these solutions back into the original equation and see if both solutions are valid!

To solve an absolute value equation, one must first rewrite the problem two different ways.

One is

and the other is

.

Then, solve each equation for v.

Your answers are 8 and -5.

To solve for x, we first must isolate the absolute value on one side of the equation:

Remember that an absolute value makes whatever is inside of it positive, so this equation is valid for both what is given inside the absolute value, and also the negative of what is inside:

To solve for x, we first must isolate the absolute value:

The absolute value makes whatever is inside of it positive, so the equation is valid for what is given, as well as for the negative of what is inside:

Now, solve for x for both equations:

Both equations get us this result.

Break up the absolute value into its positive and negative components.

The equations are:

Solve the first equation.  Add 4 on both sides.

Divide by three on both sides.

The first solution is:  

Solve the second equation.  Divide by negative one on both sides to move the negative from left to right.

Add 4 on both sides.

Divide by three on both sides.

The solutions are:  

To solve, we must first isolate the absolute value on one side:

Next, we must remember that the equation holds true for both the positive and negative of what is inside the absolute value sign, because the absolute value makes whatever is inside of it positive:

Solving for x, we get

One can plug the solutions back into the original equation to confirm. 

Solve by first dividing negative two on both sides.  This will isolate the absolute value term.

Do NOT continue with this problem!  There are no cases where an absolute value of a number will equal to negative four. 

The answer to this equation is:  

Break up the absolute value and split this equation into its positive and negative components.

Solve the first equation.  Add 18 on both sides.

Simplify both sides.  One of the answers is:

Solve the second equation.  Divide both sides by negative one.

The equation becomes:

Add 18 on both sides.

The other solution is:

The answer is: