Questions: Use the definition of absolute value to solve the following equation y + 7 = 3 y = (smaller value) y = (larger value)

Transcript text: Use the definition of absolute value to solve the following equ \[ \begin{array}{l} \qquad|y|+7=3 \\ y=\square \text { (smaller value) } \\ y=\square \text { (larger value) } \end{array} \] Additional Materials Tutorial Submit Answer

Solution

Solution Steps

To solve the equation \(|y| + 7 = 3\), we first isolate the absolute value term. Then, we consider the two possible cases for the absolute value: \(y\) could be positive or negative. We solve for \(y\) in both cases.

Step 1: Isolate the Absolute Value Term

Given the equation: \[ |y| + 7 = 3 \] First, isolate the absolute value term by subtracting 7 from both sides: \[ |y| = 3 - 7 \]

Step 2: Simplify the Equation

Simplify the right-hand side: \[ |y| = -4 \]

Step 3: Analyze the Absolute Value

Since the absolute value of a number cannot be negative, there are no real solutions to the equation.