Absolute Value Equations - College Algebra

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

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

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

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

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

and

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

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,

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.

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.

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

Since absolute values can come from either negative or positive values, two equations need to be set up and solved for.

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:

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.

We have to set up two equations, which are.

Now lets solve for x in each equation.

So the solutions are and

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

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

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

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

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

and

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

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,

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.

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

Since absolute values can come from either negative or positive values, two equations need to be set up and solved for.

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:

We have to set up two equations, which are.

Now lets solve for x in each equation.

So the solutions are and

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

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