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

1 answer

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: \[ 48 = 48 \]