Question

solve for z.
6z + z - 4z + 4z - 5z = 14
z =

Explanation:

Step1: Combine like terms

First, we combine the terms with \( z \) on the left side. Let's calculate the coefficients: \( 6 + 1 - 4 + 4 - 5 \).
\( 6z + z - 4z + 4z - 5z=(6 + 1 - 4 + 4 - 5)z \)
Calculating the sum inside the parentheses: \( 6 + 1 = 7 \), \( 7 - 4 = 3 \), \( 3 + 4 = 7 \), \( 7 - 5 = 2 \). So we have \( 2z = 14 \).

Step2: Solve for \( z \)

To isolate \( z \), we divide both sides of the equation \( 2z = 14 \) by 2.
\( z=\frac{14}{2} \)
Simplifying the right side, \( \frac{14}{2}=7 \).

Answer:

\( z = 7 \)