91Ó°ÊÓ

When solving linear equations, isolating the variable is usually the first step. This process means getting the variable you're solving for by itself on one side of the equation. This helps in identifying the value of the variable more directly. For the given equation, \( \frac{m}{3} + 10 = 8 \), the goal is to isolate \( m \) on the left side.

To begin, eliminate the constant by subtracting 10 from both sides of the equation. This operation moves the 10 away from the variable term, simplifying the equation to \( \frac{m}{3} = -2 \). Remember to always perform the same operation on both sides of the equation to maintain equality. This step clears out any additional terms that are added or subtracted from the side containing the variable. By following this method, isolating the variable becomes a straightforward task.

Once you've found what you believe is the solution to a linear equation, it's important to verify its correctness. This process involves substituting the found value back into the original equation and ensuring that both sides are equal.

After calculating that \( m = -6 \) is the solution, plug it back into the original equation: \( \frac{-6}{3} + 10 = 8 \). By simplifying, you do \( -2 + 10 \), which results in 8, confirming that the left side equals the right side of the original equation. This step is crucial, as it catches potential errors in your calculations. Verification acts as a safety check, ensuring your solution is both mathematically logical and precise.

Handling fractions in equations can be intimidating, but with the right approach, it becomes simple. Equations like \( \frac{m}{3} + 10 = 8 \) include fractions, requiring proper techniques to solve them effectively.

The main goal is often to eliminate the fraction by multiplying every term by the denominator. For instance, multiply both sides of \( \frac{m}{3} = -2 \) by 3 to eliminate the fraction. This action transforms the equation into \( m = -6 \). By doing so, you revert the variable term to a whole number, simplifying the problem and making further steps easier.

In summary, being methodical with fractions by multiplying terms correctly helps break down the problem into simpler parts. This simplifies your path towards isolating the variable and ultimately solving the equation.