Jordan used the distributive property to write an expression that is equivalent to [tex]\(6c - 48\)[/tex].
Is [tex]\(6c - 48\)[/tex] equivalent to [tex]\(6(c - 48)\)[/tex]?
A. Yes, Jordan's work is correct. B. No, Jordan forgot to divide 48 by 6. C. No, Jordan forgot to subtract 6 from 48. D. No, Jordan forgot to multiply 6 and 48.
Let's analyze Jordan's work step by step to determine if it is correct or incorrect.
Jordan's original expression is: [tex]\[ 6c - 48 \][/tex]
Jordan states that it is equivalent to: [tex]\[ 6(c - 48) \][/tex]
To verify this, we can use the distributive property to expand Jordan's expression. The distributive property tells us that: [tex]\[ a(b - c) = ab - ac \][/tex]
In Jordan's expression, [tex]\( a = 6 \)[/tex], [tex]\( b = c \)[/tex], and [tex]\( c = 48 \)[/tex], so if we expand it we get: [tex]\[ 6(c - 48) = 6c - 6 \cdot 48 \][/tex]
So, the expanded form of Jordan's expression is: [tex]\[ 6c - 288 \][/tex]
Now let's compare this to the original expression: [tex]\[ 6c - 48 \][/tex]
We can see that: [tex]\[ 6c - 48 \neq 6c - 288 \][/tex]
Therefore, Jordan's expression [tex]\( 6(c - 48) \)[/tex] is not equivalent to [tex]\( 6c - 48 \)[/tex]. It is clear that Jordan made a mistake. Specifically, Jordan forgot to divide 48 by 6 before placing it inside the parentheses.
Among the given choices, the correct answer is: No, Jordan forgot to divide 48 by 6.
