Problem 82 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$-8(3+11)=-24+(-88)$$

Step-by-Step Solution

Answer

The property illustrated in this equation is the Distributive Property.

Step 1: Recognize the equation structure

The given equation is \(-8(3+11)=-24+(-88)\). The left hand side of the equation involves multiplication operation by associating \(-8\) with the sum of \(3\) and \(11\), and the right hand side involves addition of \(-24\) and \(-88\). The association, in this case, is multiplication.

Step 2: Identify the property at play

Seeing the left hand side, it applies that \(-8\) is multiplied to both \(3\) and \(11\) individually. This method of breaking down the multiplication over addition or subtraction represents the distributive property.

Step 3: Confirm the representation

To confirm it represents distributive property, the equation can be rewritten by applying reverse of distributive law on the right-hand side as: \(-8*3 + -8*11 = -24 + -88\), which simplifies to \(-8*(3+11) = -24 + -88\). It proves to be identical to the initial equation.