Question

1. for what value of p makes the following equation true?

\frac{p - 4}{7} = \frac{3p + 1}{5}
type a response

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{p - 4}{7}=\frac{3p+1}{5}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\) for \(b
eq0\) and \(d
eq0\)) gives us \(5(p - 4)=7(3p + 1)\).

Step2: Expand both sides

Expand the left - hand side: \(5\times p-5\times4 = 5p-20\).
Expand the right - hand side: \(7\times3p+7\times1=21p + 7\).
So the equation becomes \(5p-20 = 21p+7\).

Step3: Move the terms with p to one side and constants to the other

Subtract \(5p\) from both sides: \(5p-5p - 20=21p-5p + 7\), which simplifies to \(-20 = 16p+7\).
Then subtract 7 from both sides: \(-20 - 7=16p+7 - 7\), so \(-27 = 16p\).

Step4: Solve for p

Divide both sides by 16: \(p=\frac{-27}{16}\).

Answer:

\(p =-\frac{27}{16}\)