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

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
Transcript text: 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. \[ 22 z-21 z-19=-14 \]
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Solution

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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.

Step 1: Simplify the Equation

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: \[ z - 19 = -14 \]

Step 2: Isolate the Variable

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

Final Answer

\[ \boxed{z = 5} \]

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