Question

1. which equation is the same as $3(2p + 4) - (3p - 4) = 43$?

$2p + 16 = 43$
$3p + 16 = 43$
$2p + 8 = 43$
$3p + 8 = 43$

Explanation:

Step1: Expand the left - hand side

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(3(2p + 4)\) and \(-(3p - 4)\).
For \(3(2p+4)\), we have \(3\times2p+3\times4 = 6p + 12\).
For \(-(3p - 4)\), we have \(-3p+4\) (because \(-(a - b)=-a + b\)).

Step2: Combine like terms

Now, we combine the expanded terms:
\((6p + 12)+(-3p + 4)=6p-3p+12 + 4\)
Combining the \(p\) - terms: \(6p-3p = 3p\)
Combining the constant terms: \(12 + 4=16\)
So the left - hand side simplifies to \(3p + 16\), and the equation becomes \(3p+16 = 43\).

Answer:

B. \(3p + 16 = 43\) (assuming the second option is \(3p + 16 = 43\))