Question

jordan used the distributive property to write an expression that is equivalent to 6c - 48.
6c - 48 is equivalent to 6(c - 48)
is jordan’s work correct? choose the correct answer.
○ yes, jordan’s work is correct.
○ no, jordan forgot to divide 48 by 6.
○ no, jordan forgot to subtract 6 from 48.
○ no, jordan forgot to multiply 6 and 48.

Explanation:

To determine if Jordan's work is correct, we use the distributive property: \(a(b - c)=ab - ac\). For \(6(c - 48)\), distributing 6 gives \(6\times c-6\times48 = 6c - 288\), not \(6c - 48\). Wait, no—wait, the original expression equivalent to \(6c - 48\) using distributive property should be \(6(c - 8)\) (since \(6\times8 = 48\)), but the problem says Jordan wrote \(6(c - 48)\) as equivalent to \(6c - 48\). Wait, no, let's re - read. The problem is: "Jordan used the distributive property to write an expression that is equivalent to \(6c - 48\). \(6c - 48\) is equivalent to \(6(c - 48)\). Is Jordan’s work correct? Choose the correct answer."

Using the distributive property \(a(b - c)=ab - ac\), if we have \(6(c - x)=6c-6x\). We want \(6c - 6x=6c - 48\), so \(6x = 48\), and \(x = 8\). But Jordan wrote \(6(c - 48)=6c-6\times48=6c - 288
eq6c - 48\). Wait, maybe I misread. Wait, the options: "No, Jordan forgot to divide 48 by 6." Let's see: To get from \(6c - 48\) to \(6(c - x)\), we know that \(6x = 48\), so \(x=\frac{48}{6}=8\). So Jordan should have \(6(c - 8)\), but he has \(6(c - 48)\). So he forgot to divide 48 by 6 (to get the correct term inside the parentheses). So the correct option is "No, Jordan forgot to divide 48 by 6."

Answer:

B. No, Jordan forgot to divide 48 by 6.