41 = 270/(14 + p)
Understand the Problem
The question is asking us to solve the equation 41 = 270/(14 + p) for the variable p. To do this, we will first multiply both sides by (14 + p) to eliminate the fraction, and then isolate p to find its value.
Answer
$p \approx -7.41$
Answer for screen readers
The value of $p$ is approximately $-7.41$.
Steps to Solve
- Multiply both sides by (14 + p)
To eliminate the fraction, we start by multiplying both sides of the equation by $(14 + p)$.
$$ 41(14 + p) = 270 $$
- Distribute on the left side
We then distribute the 41 on the left side of the equation:
$$ 574 + 41p = 270 $$
- Isolate the variable term
Next, we need to isolate the term with $p$. We do this by subtracting 574 from both sides:
$$ 41p = 270 - 574 $$
- Calculate the right side
Now, perform the subtraction on the right side:
$$ 41p = -304 $$
- Solve for p
Finally, divide both sides by 41 to solve for $p$:
$$ p = \frac{-304}{41} $$
- Simplify the fraction
To simplify the division:
$$ p = -7.41 \quad \text{(approximately)} $$
The value of $p$ is approximately $-7.41$.
More Information
The solution shows that the variable $p$ has a negative value. Understanding how to manipulate equations and isolate variables helps solve similar algebraic equations effectively.
Tips
- Forgetting to distribute correctly can lead to incorrect results. Always double-check your distribution steps.
- Not isolating the variable correctly can lead to errors; ensure you perform inverse operations correctly.
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