Problem 67 - Algebra 1: Concepts and Skills

Question

Solve the equation. \(|x|=3\)

Step-by-Step Solution

Answer

The solutions to the given equation are \(x=3\) and \(x=-3\).

Step 1: Understand Absolute Value

By definition, absolute value refers to the non-negative value of a real number without regard to its sign. It means, \(|x|\) is equal to \(x\) if \(x\) is greater than or equal to 0. But, \(|x|\) is equal to \(-x\) if \(x\) is less than 0.

Step 2: Apply Absolute Value Definition

We can set up two separate equations to solve for \(x\) given \(|x|=3\). The first one is \(x=3\) and the second one is \(-x=3\).

Step 3: Solve for x

Solving \(x=3\) is straightforward, \(x\) is 3 for the first equation. For the second equation \(-x=3\), dividing both sides by -1, we get \(x=-3\).