Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( p = -\frac{7}{8} \) and \( p = -\frac{15}{8} \).
Solution
To solve the equation:
\[
|8p + 11| - 7 = -3
\]
**Step 1: Isolate the Absolute Value**
Add 7 to both sides of the equation to isolate the absolute value:
\[
|8p + 11| = -3 + 7
\]
\[
|8p + 11| = 4
\]
**Step 2: Set Up Two Cases**
The absolute value equation \( |A| = B \) has two possible cases:
1. \( A = B \)
2. \( A = -B \)
Applying this to our equation:
1. **Case 1:**
\[
8p + 11 = 4
\]
Subtract 11 from both sides:
\[
8p = 4 - 11
\]
\[
8p = -7
\]
Divide both sides by 8:
\[
p = -\frac{7}{8}
\]
2. **Case 2:**
\[
8p + 11 = -4
\]
Subtract 11 from both sides:
\[
8p = -4 - 11
\]
\[
8p = -15
\]
Divide both sides by 8:
\[
p = -\frac{15}{8}
\]
**Step 3: Conclusion**
The solutions to the equation are:
\[
p = -\frac{7}{8} \quad \text{and} \quad p = -\frac{15}{8}
\]
**Verification:**
It's always good practice to verify the solutions by plugging them back into the original equation.
1. **For \( p = -\frac{7}{8} \):**
\[
|8(-\frac{7}{8}) + 11| - 7 = |-7 + 11| - 7 = |4| - 7 = 4 - 7 = -3
\]
The equation holds true.
2. **For \( p = -\frac{15}{8} \):**
\[
|8(-\frac{15}{8}) + 11| - 7 = |-15 + 11| - 7 = |-4| - 7 = 4 - 7 = -3
\]
The equation holds true.
Both solutions are valid.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the equation \( |8 p + 11| - 7 = -3 \), first, we add 7 to both sides to isolate the absolute value: \( |8 p + 11| = 4 \). Now we can split this into two cases: 1. \( 8p + 11 = 4 \) 2. \( 8p + 11 = -4 \) For the first case: \( 8p = 4 - 11 \) \( 8p = -7 \) \( p = -\frac{7}{8} \). For the second case: \( 8p = -4 - 11 \) \( 8p = -15 \) \( p = -\frac{15}{8} \). So the solutions are \( p = -\frac{7}{8} \) and \( p = -\frac{15}{8} \). To verify, plug these values back into the original equation and check if both sides are equal!
