Question

solve the equation. what is the value of p?
7 - 3(1p + 2) = 3p - 5
p = \square

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(-3(1p + 2)\) as \(-3p-6\). So the left side of the equation \(7-3(1p + 2)\) becomes \(7-3p - 6\). Simplifying \(7 - 6\) gives \(1-3p\). Now the equation is \(1-3p=3p - 5\).

Step2: Add \(3p\) to both sides

To get all the \(p\) terms on one side, we add \(3p\) to both sides of the equation. \((1-3p)+3p=(3p - 5)+3p\). Simplifying both sides, the left side becomes \(1\) (since \(-3p+3p = 0\)) and the right side becomes \(6p-5\). So now we have \(1=6p - 5\).

Step3: Add 5 to both sides

To isolate the term with \(p\), we add \(5\) to both sides. \(1 + 5=6p-5 + 5\). Simplifying, the left side is \(6\) and the right side is \(6p\) (since \(-5 + 5=0\)). So we have \(6 = 6p\).

Step4: Divide both sides by 6

To solve for \(p\), we divide both sides of the equation \(6 = 6p\) by \(6\). \(\frac{6}{6}=\frac{6p}{6}\). Simplifying, we get \(1=p\) or \(p = 1\).

Answer:

\(1\)