Question

What is the equation of this multistep inequalities problem: 3p - 2(p - 4) < p - (2 - 3p)?

a) 3p - 2p + 8 < p - 2 + 3p
b) 3p - 2p - 8 < p - 2 + 3p
c) 3p - 2p - 8 > p - 2 + 3p
d) 3p + 2(p - 4) > p + (2 - 3p)

Answer 1

The correct equation for the given multistep inequality problem is 3p - 2p + 8 < p - 2 + 3p. This is obtained by distributing the negative signs and combining like terms, which corresponds to option a.

Step-by-step explanation:

The equation for the multistep inequality problem is obtained by simplifying the given inequality 3p - 2(p - 4) < p - (2 - 3p). To solve this, we distribute and combine like terms on both sides of the inequality.

1. Distribute the -2 across (p - 4) to get 3p - 2p + 8.
2. Distribute the -1 across (2 - 3p), remembering to reverse the sign for each term, yields p - 2 + 3p.
3. Combine like terms to simplify the inequality: 3p - 2p + 8 < p - 2 + 3p simplifies to p + 8 < 4p - 2.

Comparing with the options provided, the correct equation that represents this inequality is option a: 3p - 2p + 8 < p - 2 + 3p.