91Ó°ÊÓ

When solving linear equations, it is crucial to check the solution to ensure it is correct. After finding the value of the variable, substitute that value back into the original equation. This tests if the equation holds true with the calculated value. In our example, after solving for \( n \), we substitute \( n = 8 \) back into the equation: 1. Replace \( n \) with 8: \[ 1.8 = 1.2(8) - 7.8. \]2. Calculate the right-hand side: - First, multiply: \( 1.2 imes 8 = 9.6 \). - Then, subtract \( 7.8 \) from \( 9.6 \), which equals \( 1.8 \).3. Both sides of the equation calculate to \( 1.8 \), so the solution is verified as correct.
This step confirms that you have not made any mistakes during the solving process, ensuring accuracy in your work.

In solving equations, combining like terms is a fundamental algebraic skill. Like terms are terms that have the same variable raised to the same power. To simplify, you should add or subtract these terms. In our equation \(1.8 = 1.2n - 7.8\), like terms are not directly visible, but you still consolidate the equation by moving constants to one side.

• On the left side, we started with \(1.8\).
• To get rid of the constant \(-7.8\) on the right side, add \(7.8\) to both sides.
• This results in \(1.8 + 7.8 = 1.2n\).

This step minimizes the number of terms and lays the foundation for isolating the variable, leading to a simpler equation that is easier to solve.

The goal when solving a linear equation is to isolate the variable on one side of the equation. This means having the variable by itself, with no coefficients or constants. In our example, after combining like terms, we have \(9.6 = 1.2n\).

• Here, the variable \(n\) is not isolated because it is multiplied by \(1.2\).
• To isolate \(n\), divide both sides by the coefficient \(1.2\).
• This gives you: \[\frac{9.6}{1.2} = n,\] resulting in \( n = 8 \).

By isolating the variable, you have now found the solution to the equation. Remember, isolating the variable is a key step in solving any equation, as it directly provides you with the value of the unknown.