Question

So the equation state whether the equation is a contradiction, an identity, or conditional equation
9(z+2)=8(z-6)+z

Answer 1

To determine whether the equation \(9(z+2)=8(z-6)+z\) is a contradiction, an identity, or a conditional equation, we need to simplify both sides.

1. **Expand both sides**:

Left Side:
\[
9(z+2) = 9z + 18
\]

Right Side:
\[
8(z-6) + z = 8z - 48 + z = 9z - 48
\]

2. **Set both sides equal**:
\[
9z + 18 = 9z - 48
\]

3. **Subtract \(9z\) from both sides**:
\[
18 = -48
\]

This statement \(18 = -48\) is false.

Since we arrived at a false statement after simplifying the equation, we conclude that the original equation is a **contradiction**.