How to solve absolute value equations

|x – 3| = 2 means that it can be separated into x – 3 = 2 and x – 3 = –2.

So both x = 5 and x = 1 work.

x – 3 = 2 Add 3 to both sides to get x = 5

x – 3 = –2 Add 3 to both sides to get x = 1

Because of the absolute value signs,

or

Subtract 2 from both sides of both equations:

or

or

There are two answers to this problem:

and

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

The first step is to split the absolute value into two equations, one case for when the inside of the absolute value will be negative and one case for when the inside of the absolute value will be positive.

Positive case:

First subtracting 2 and 4x from both sides:

dividing both sides by -2:

Negative case:

First move the negative to the other side:

Next, add 4x and subtract 2 from both sides:

Finally, divide both sides by 6 and reducing:

Thus the solutions are:

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, .

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

.

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

Divide both sides by , we get .

Final answer is .

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,

.