Question

the equation 10(3c + 8) = 6(5c + 12) + 8 has infinitely many solutions. how can you tell? if you subtract 30c from both sides, the variables all cancel out. when simplified, both sides have the same variable term and the same constant term, so they match. both sides have distribution, so they match. both sides have 8, so the constant terms match.

Explanation:

Step1: Expand both sides

First, expand the left - hand side: $10(3c + 8)=30c+80$. Expand the right - hand side: $6(5c + 12)+8 = 30c+72 + 8=30c + 80$.

Step2: Analyze the simplified equation

The simplified equation is $30c+80=30c + 80$. When we subtract $30c$ from both sides, we get $80 = 80$, a statement that is always true regardless of the value of $c$. This means the equation has infinitely many solutions because both sides have the same variable term ($30c$) and the same constant term ($80$).

Answer:

B. When simplified, both sides have the same variable term and the same constant term, so they match.