Questions: Solve the linear equation using equivalent equations to isolate the variable. Express your solution as an integer, as a simplified fraction, or as a decimal number. 22z - 21z - 19 = -14

Solution Steps

To solve the linear equation \(22z - 21z - 19 = -14\), we first simplify the left side by combining like terms. This will give us a simpler equation in terms of \(z\). Then, we isolate \(z\) by performing basic arithmetic operations to solve for it.

The given equation is: \[ 22z - 21z - 19 = -14 \] First, combine like terms on the left side: \[ (22z - 21z) - 19 = z - 19 \] Thus, the equation simplifies to: \[ z - 19 = -14 \]

To solve for \(z\), add 19 to both sides of the equation: \[ z - 19 + 19 = -14 + 19 \] This simplifies to: \[ z = 5 \]

Final Answer