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Fractions can sometimes make algebraic equations look complicated, but they're easy to manage with a basic understanding of fractions. When an equation is given in the form of a fraction, like \( \frac{y}{0.6} = -4.4 \), the fraction here represents division. For equations involving fractions, the main goal is to clear the fraction to make the equation simpler and solve for the variable. This is achieved by multiplying both sides of the equation by the denominator of the fraction.

• Identify the denominator in the fraction.
• Multiply every term in the equation by this denominator.

By applying this technique to our example equation \(\frac{y}{0.6} = -4.4\), we multiply both sides by \(0.6\), removing the fraction and leaving us with \( y = -4.4 \times 0.6 \), making it simpler to solve.

Solving linear equations involves finding the value of the unknown variable that makes the equation true. Linear equations are equations of the first degree, meaning the variable is only raised to the power of one. Once we have addressed any fractions, solving the equation becomes straightforward.
Use these steps to solve a linear equation:

• Simplify both sides of the equation if necessary, by combining like terms or clearing fractions.
• Isolate the variable on one side of the equation.
• If required, perform additional arithmetic operations to solve for the variable.

For the equation \( y = -2.64 \) derived from solving \( \frac{y}{0.6} = -4.4 \), the steps were initiated by clearing the fraction and simplifying the expression. This direct and logical approach aids in effectively finding the solution to linear equations.

After solving a linear equation, verifying the solution ensures that the computed value satisfies the original equation. To verify a solution, you substitute the value of the variable back into the original equation and check if both sides of the equation are equal.
Here’s a practical approach to verification:

• Take the solution found for the variable.
• Substitute this value back into the original equation.
• Solve the equation using these values to check if the equation holds true.

In our example, the solution \( y = -2.64 \) was substituted back into the equation \( \frac{y}{0.6} = -4.4 \). By computing \( \frac{-2.64}{0.6} \), we could confirm that both sides equal \(-4.4\). This confirmed the accuracy of the solution, which is an essential step to ensure confidence in solving algebraic equations correctly.