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.
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Distribute \(6\) to both \(11\) and \(-3\) on the left side: \[ 6(11 - 3) = 6 \cdot 11 + 6 \cdot (-3) = 66 - 18 \]
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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: \[ 48 = 48 \]