Problem 46 - Beginning and Intermediate Algebra

Question

Write an absolute value equation that means \(y\) is 6 units from zero.

Step-by-Step Solution

Answer

The absolute value equation that means \(y\) is 6 units from zero is: \( |y| = 6 \).

Step 1: Set up the equation with an absolute value function

Since the absolute value of \(y\) must be 6 units from zero, we can write the equation as: \( |y| = 6 \)

Step 2: Solve for y

Since the absolute value function tells us the distance from zero, there are two solutions for \(y\). When the distance is positive, and when the distance is negative. We can write this as two separate equations: \( y = 6 \) and \( y = -6 \) These two solutions represent the two possible values of \(y\) that are 6 units away from zero. The final equation that means \(y\) is 6 units from zero is: \( |y| = 6 \)