91Ó°ÊÓ

Equation rearrangement is a powerful skill that allows us to manipulate an equation to isolate a variable, making it easier to solve. In this exercise, our goal was to solve for the variable \(x\). To begin, we had the equation \(3.6x = 2.9x + 6.3\). Our first step was to move all terms involving \(x\) to one side. This step is crucial because it simplifies the equation. We do this by performing an operation on both sides of the equation. Here, we subtracted \(2.9x\) from both sides. The result was the rearranged equation: \(0.7x = 6.3\). Rearranging ensures that terms are grouped effectively, isolating the variable of interest. It helps in reducing complexity and avoids errors as we proceed to the next steps in solving the equation. The key takeaway here is: rearranging puts equations in a clearer form, ready for straightforward solving.

The concept of like terms is essential when working with algebraic expressions. Like terms are terms that have the same variable raised to the same power. Only coefficients differ among like terms.In our exercise, we encountered like terms early on: \(3.6x\) and \(2.9x\). These terms both have the variable \(x\), making them like terms. When simplifying equations, we combine like terms to condense the expression, making it easier to solve.

• For \(3.6x\) and \(2.9x\), subtraction allowed us to combine them: \(3.6x - 2.9x\) simplifies to \(0.7x\).
• This process helps streamline the equation and directly influences the steps required to isolate \(x\).

Recognizing and handling like terms effectively simplifies the problem, saving time and minimizing errors in calculations.

Verifying solutions is a critical final step in solving equations. It confirms that the solution is correct and applicable to the original equation.After solving for \(x\) and finding \(x = 9\), we need to check if this value satisfies the original equation \(3.6x = 2.9x + 6.3\). To verify:

• Substitute \(x = 9\) back into the original equation.
• Calculate each side: \(3.6 \times 9\) and \(2.9 \times 9 + 6.3\).

Both sides equaled \(32.4\), proving our solution correct. Verification is essential as it acts as a final check against careless errors or misunderstanding of the problem. This step reassures us that our process was sound and provides confidence in the results obtained.