Certainly! Let's go through the equation step-by-step to understand what is wrong:
The given equation is:
[tex]\[ 2(n + 3) = 2n + 3 \][/tex]
To determine the mistake, we need to apply the distributive property of multiplication over addition to the left-hand side of the equation. The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex].
Let's apply this property to the left-hand side of the equation [tex]\( 2(n + 3) \)[/tex]:
[tex]\[ 2(n + 3) = 2 \cdot n + 2 \cdot 3 \][/tex]
Now, we perform the multiplication:
[tex]\[ 2 \cdot n = 2n \][/tex]
[tex]\[ 2 \cdot 3 = 6 \][/tex]
So, the left-hand side simplifies to:
[tex]\[ 2n + 6 \][/tex]
This means the correct equation should be:
[tex]\[ 2(n + 3) = 2n + 6 \][/tex]
Now, let's compare this with the original equation given:
[tex]\[ 2(n + 3) = 2n + 3 \][/tex]
We can see that the original equation has:
[tex]\[ 2n + 3 \][/tex]
instead of the correct:
[tex]\[ 2n + 6 \][/tex]
So, the mistake is that the number 2 was not properly distributed to both [tex]\( n \)[/tex] and 3. It seems like the number 2 was only distributed to [tex]\( n \)[/tex] but not to the 3.
To sum up, the error in the original equation is due to an incorrect application of the distributive property. The correct equation after distributing should be:
[tex]\[ 2(n + 3) = 2n + 6 \][/tex]
