Questions: 8+4y=32

8+4y=32
Transcript text: $|8+4y|=32$
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Solution

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Solution Steps

To solve the equation \( |8 + 4y| = 32 \), we need to consider the definition of absolute value. The equation can be split into two separate linear equations: \( 8 + 4y = 32 \) and \( 8 + 4y = -32 \). We will solve each of these equations for \( y \).

Step 1: Understand the Absolute Value Equation

The given equation is \( |8 + 4y| = 32 \). The absolute value equation can be split into two separate linear equations:

  1. \( 8 + 4y = 32 \)
  2. \( 8 + 4y = -32 \)
Step 2: Solve the First Equation

For the equation \( 8 + 4y = 32 \), we solve for \( y \): \[ 4y = 32 - 8 \] \[ 4y = 24 \] \[ y = \frac{24}{4} = 6 \]

Step 3: Solve the Second Equation

For the equation \( 8 + 4y = -32 \), we solve for \( y \): \[ 4y = -32 - 8 \] \[ 4y = -40 \] \[ y = \frac{-40}{4} = -10 \]

Final Answer

\(\boxed{y = 6, -10}\)

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