Question

how could you correctly rewrite the equation 6(11-3)=4(7+5) using distributive property

Answer 1

To rewrite the equation \(6(11-3)=4(7+5)\) using the distributive property, you need to distribute the constants outside the parentheses to each term inside the parentheses.

1. Distribute \(6\) to both \(11\) and \(-3\) on the left side:
\[
6(11 - 3) = 6 \cdot 11 + 6 \cdot (-3) = 66 - 18
\]

2. Distribute \(4\) to both \(7\) and \(5\) on the right side:
\[
4(7 + 5) = 4 \cdot 7 + 4 \cdot 5 = 28 + 20
\]

Now, after applying the distributive property:

The left side:
\[
6(11-3) = 66 - 18
\]

The right side:
\[
4(7+5) = 28 + 20
\]

Putting it all together, the rewritten equation using the distributive property is:
\[
66 - 18 = 28 + 20
\]

You can combine the terms on each side:
- On the left side, \(66 - 18 = 48\).
- On the right side, \(28 + 20 = 48\).

Therefore, both sides simplify to \(48\), confirming the correctness of the distribution. The final rewritten equation is:
\[
48 = 48
\]