Question

1. what is the value of p in the equation \\(\frac{1}{4}(3p + 12) = \frac{3}{4}(p - 16)\\)? \\(p = 3\\) \\(p = -12\\) no solution infinitely many solutions

Explanation:

Step1: Eliminate denominators

Multiply both sides of the equation $\frac{1}{4}(3p + 12)=\frac{3}{4}(p - 16)$ by 4 to get rid of the fractions:
$4\times\frac{1}{4}(3p + 12)=4\times\frac{3}{4}(p - 16)$
Simplify to: $3p + 12 = 3(p - 16)$

Step2: Expand the right side

Expand $3(p - 16)$ using the distributive property:
$3p + 12 = 3p - 48$

Step3: Subtract \(3p\) from both sides

Subtract \(3p\) from each side:
$3p - 3p + 12 = 3p - 3p - 48$
Simplify to: $12 = -48$

Since \(12 = -48\) is a false statement, the equation has no solution.

Answer:

no solution