Problem 84 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$(x+4)+[-(x+4)]=0$$

Step-by-Step Solution

Answer

The property illustrated by the equation is the Additive Inverse property.

Step 1: Analyze the equation

The given equation is \((x+4)+[-(x+4)]=0\). This equation can be broken down by dealing with the [-] sign that negates the expression within the brackets \(-(x+4)\).

Step 2: Apply Negative Sign

Applying the negative sign to the expression \((x+4)\) results in \(-(x+4) = -x - 4\). Substituting back into the equation gives \((x+4) - (x+4) = 0\)

Step 3: Combine Like Terms

When we combine like terms, we get \(x + 4 - x - 4\). Both \(x\) and \(-x\) cancel each other out, as do \(4\) and \(-4\). This would result in the equation \(0=0\)

Step 4: Identify Property

From the result, we can see that this is an illustration of the Additive Inverse property of numbers. The Additive Inverse property states that for any number \(a\), there exists a number \(-a\) such that when the two are added, the result is \(0\). This can be seen here where \((x+4)\) was added to its inverse \(-x - 4\) which resulted in \(0\)