91Ó°ÊÓ

When working with linear equations, one of the first tasks is often to simplify the expression by combining like terms. Like terms are terms that have the same variable raised to the same power. For example, in the exercise \(0.4x - 0.9x - 6 = 19\), the like terms are \(0.4x\) and \(-0.9x\). Both have the variable \(x\) and can be combined.
The process of combining them is straightforward: we simply add or subtract their coefficients (the numbers in front of the variables). Here, adding \(-0.9\) to \(0.4\) gives us \(-0.5\). Our equation then simplifies to \(-0.5x - 6 = 19\).
By combining like terms, we make the equation easier to solve, eliminating unnecessary complexity and focusing on the things that matter.

Once you have combined like terms, the next step is solving the equation. This involves isolating the variable term on one side to find the value of the unknown. For the equation \-0.5x - 6 = 19\, our goal is to isolate \(-0.5x\).
We begin by getting rid of the constant term \(-6\) on the left side. This is done by adding 6 to both sides, giving us \(-0.5x = 25\). Next, we solve for \(x\) by dividing both sides by \(-0.5\), resulting in \(-50\). This approach keeps the balance of the equation, maintaining its truth.
Remember, in any linear equation, our objective is to make the equation as simple as possible while isolating the variable of interest.

The final step in solving any equation is checking the solution. This confirms that the solution is indeed correct. To check, substitute the solution back into the original equation and ensure that both sides are equal.
In our case, substituting \(x = -50\) into the original equation \(0.4x - 0.9x - 6 = 19\), we compute: \(0.4(-50) = -20\) and \(-0.9(-50) = 45\).
Inserting these values gives us \(-20 + 45 - 6\), which simplifies to \(19\). This matches the right side of the original equation, confirming that \(x = -50\) is the correct solution.
Checking is an essential step because it verifies accuracy and builds confidence in your solving process.