Question

Solve the absolute value equation, or indicate that the equation has no solution
|x|=3

Answer 1

3 and -3

Explanation:

Since the equation is an absolute value equation, this means no matter if you input a negative number or a positive number, it comes out positive. All we need to do is get the absolute value of x to equal 3. This means that we are to disregard any negative symbol on a number. That means that the only 2 numbers that equal 3 when inputted into x are 3 and -3.

3 would be an answer because the abolute value of 3 is just 3. 3 is already positive, so it doesn't change anything.

-3 would be an answer bcause the absolute value of -3 is 3. Since we are getting the absolute value of it, we are to disregard the negative symbol. -3 without it being negative is just 3.

Answer 2

x = 3 and x = -3

Explanation:

The absolute value of a number is its distance from zero. It is denoted by two vertical lines, like this: |x|.

So, the absolute value of 3 is 3, and the absolute value of -3 is also 3.

In order to solve the equation |x|=3, we need to consider two cases:

Case 1:

x is non-negative.

In this case, |x| = x. So, we have the equation x = 3.

Case 2:

x is negative.

In this case, |x| = -x. So, we have the equation -x = 3.

Solving the equation x = 3, we get x = 3.

Solving the equation -x = 3, we get x = -3.

Therefore, the solutions of the equation |x|=3 are x = 3 and x = -3.