Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( k = \frac{9}{5} \) or \( k = -3 \)
Solution
To solve the equation:
\[
|5k + 3| - 8 = 4
\]
Follow these steps:
1. **Isolate the Absolute Value:**
\[
|5k + 3| = 4 + 8
\]
\[
|5k + 3| = 12
\]
2. **Consider the Two Cases for the Absolute Value:**
The expression inside the absolute value can be either positive or negative.
- **Case 1:** \( 5k + 3 = 12 \)
\[
5k = 12 - 3
\]
\[
5k = 9
\]
\[
k = \frac{9}{5} \quad \text{or} \quad k = 1.8
\]
- **Case 2:** \( 5k + 3 = -12 \)
\[
5k = -12 - 3
\]
\[
5k = -15
\]
\[
k = \frac{-15}{5} \quad \text{or} \quad k = -3
\]
3. **Solutions:**
The equation has two solutions:
\[
k = \frac{9}{5} \quad \text{and} \quad k = -3
\]
\[
k = 1.8 \quad \text{and} \quad k = -3
\]
**Final Answer:**
\( k = \frac{9}{5} \) or \( k = -3 \)
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Simplify this solution The Deep Dive
To solve the equation \( |5k + 3| - 8 = 4 \), let's first isolate the absolute value: 1. Add 8 to both sides: \[ |5k + 3| = 12 \] Now, we consider the two cases for the absolute value: 2. **Case 1:** \( 5k + 3 = 12 \) - Subtract 3 from both sides: \[ 5k = 9 \] - Divide by 5: \[ k = \frac{9}{5} \] 3. **Case 2:** \( 5k + 3 = -12 \) - Subtract 3 from both sides: \[ 5k = -15 \] - Divide by 5: \[ k = -3 \] Therefore, the solutions are \( k = \frac{9}{5} \) and \( k = -3 \).
