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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.



Answer :

GinnyAnswer
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]

Now, let's calculate [tex]\( 6 \cdot 48 \)[/tex]:
[tex]\[ 6 \cdot 48 = 288 \][/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.

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