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\( y = -\frac{8}{3} \) or \( y = \frac{16}{3} \)
Solución
To solve the absolute value equation:
\[
|4 - 3y| = 12
\]
we need to consider the definition of absolute value. The absolute value of an expression equals a positive number or zero. Therefore, the equation \( |A| = B \) implies:
\[
A = B \quad \text{or} \quad A = -B
\]
Applying this to the given equation:
\[
|4 - 3y| = 12
\]
leads to two separate equations:
1. **First Case: \( 4 - 3y = 12 \)**
\[
\begin{align*}
4 - 3y &= 12 \\
-3y &= 12 - 4 \\
-3y &= 8 \\
y &= \frac{8}{-3} \\
y &= -\frac{8}{3}
\end{align*}
\]
2. **Second Case: \( 4 - 3y = -12 \)**
\[
\begin{align*}
4 - 3y &= -12 \\
-3y &= -12 - 4 \\
-3y &= -16 \\
y &= \frac{-16}{-3} \\
y &= \frac{16}{3}
\end{align*}
\]
**Solutions:**
\[
y = -\frac{8}{3} \quad \text{or} \quad y = \frac{16}{3}
\]
These are the two values of \( y \) that satisfy the original absolute value equation.
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To solve the equation \( |4 - 3y| = 12 \), we need to consider the two scenarios that arise from the absolute value: 1. \( 4 - 3y = 12 \) 2. \( 4 - 3y = -12 \) For the first equation, \( 4 - 3y = 12 \): - Subtract 4 from both sides: \[ -3y = 8 \] - Divide by -3: \[ y = -\frac{8}{3} \] For the second equation, \( 4 - 3y = -12 \): - Subtract 4 from both sides: \[ -3y = -16 \] - Divide by -3: \[ y = \frac{16}{3} \] Thus, the solutions to the equation \( |4 - 3y| = 12 \) are \( y = -\frac{8}{3} \) and \( y = \frac{16}{3} \).
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