91Ó°ÊÓ

When solving linear equations, the goal is to find the value of the variable that makes the equation true. The first step to achieve this is isolating the variable. In our exercise, we start with the equation: \( -3.4z = -9.18 \). To isolate the variable \( z \), you need to get it by itself on one side of the equation.
For our given equation, this means removing the coefficient (the number multiplying the variable).
We do this by performing operations that will cancel out the coefficient, ensuring every step is balanced by doing the same operation on both sides of the equation.
In this example, we need to divide both sides by \( -3.4 \): \[ z = \frac{-9.18}{-3.4} \].
This isolates \( z \) and sets up the equation for solving.

Understanding division in algebra is crucial for solving equations. When isolating the variable, we often need to divide to simplify the equation. In our example, we divide \( -9.18 \) by \( -3.4 \). Division of decimals can seem tricky, but it follows the same rules as whole numbers. If both numbers are negative, the result will be positive. Use a calculator or manual division to find the result:
\[ z = \frac{-9.18}{-3.4} = 2.7 \].
This step shows the value of \( z \) and ensures it satisfies the original equation.

Solving equations requires a systematic approach. Here are the basic steps to solve any linear equation:

• Identify the equation: Recognize the given equation and the variables involved.
• Isolate the variable: Use operations like addition, subtraction, multiplication, or division to get the variable alone on one side.
• Simplify the equation: Perform any necessary arithmetic to solve for the variable.
• Check your solution: Substitute the variable back into the original equation to verify the result.

Applying these steps to our example:

• Start with: \( -3.4z = -9.18 \)
• Divide both sides by \( -3.4 \): \[ z = \frac{-9.18}{-3.4} \]
• Calculate the result: \[ z = 2.7 \]
• Verify by plugging \( z = 2.7 \) into the original equation.

By following these steps, any linear equation can be solved with ease.