Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( p = \frac{19}{2} \) or \( p = 9.5 \)
Solution
To solve the equation \( 4(p - 3) = 2p + 7 \), follow these steps:
1. **Expand the Left Side**
Distribute the 4 to both terms inside the parentheses:
\[
4(p - 3) = 4p - 12
\]
So, the equation becomes:
\[
4p - 12 = 2p + 7
\]
2. **Move All Terms Involving \( p \) to One Side**
Subtract \( 2p \) from both sides to get all \( p \)-terms on the left:
\[
4p - 2p - 12 = 7
\]
Simplify:
\[
2p - 12 = 7
\]
3. **Isolate the \( p \)-Term**
Add 12 to both sides to isolate the term with \( p \):
\[
2p - 12 + 12 = 7 + 12
\]
Simplify:
\[
2p = 19
\]
4. **Solve for \( p \)**
Divide both sides by 2:
\[
p = \frac{19}{2}
\]
\[
p = 9.5
\]
**Final Solution:** \( p = \frac{19}{2} \) or \( p = 9.5 \)
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To solve the equation \( 4(p-3) = 2p + 7 \), start by distributing the 4 on the left side: \[ 4p - 12 = 2p + 7. \] Next, isolate the variable \( p \) by subtracting \( 2p \) from both sides: \[ 4p - 2p - 12 = 7 \] which simplifies to: \[ 2p - 12 = 7. \] Now, add 12 to both sides: \[ 2p = 19. \] Finally, divide by 2: \[ p = 9.5. \] So the solution is \( p = 9.5 \). (b) To verify your solution, plug \( p = 9.5 \) back into the original equation. The left side becomes: \[ 4(9.5 - 3) = 4(6.5) = 26. \] The right side becomes: \[ 2(9.5) + 7 = 19 + 7 = 26. \] Both sides equal 26, confirming that \( p = 9.5 \) is correct!
