91Ó°ÊÓ

When solving linear equations, one of the essential skills is combining like terms. Like terms are terms in an equation that have the same variable raised to the same power. In our equation \[-x + 7 = 5x - 6\],we observe terms involving the variable \(x\). These terms are \[-x\] and \[5x\].
Combining them helps simplify the equation.
To do this, we can add \(x\) to both sides to remove \(-x\) from the left. This adjustment gives us a cleaner equation:\[7 = 6x - 6\].
By gathering all terms involving the same variable, we make it easier to isolate and solve for the variable in the forthcoming steps.

Once we've combined like terms, the next step is isolating the variable. This means getting the variable on one side of the equation by itself. In our example,\[7 = 6x - 6\],
our goal is to have \(x\) as a standalone term on one side. First, eliminate the constant term from the side of the equation where the variable sits.
To do so, we add 6 to both sides to counteract the \(-6\), resulting in:\[13 = 6x\].
Now, \(6x\) is plainly alone on one side, with the constants collected on the other side. This makes it much easier to uncover the value of \(x\) in the final step.

Rearranging the equation is a strategic step that allows us to simplify and solve equations more effectively. Starting with an equation like\[-x + 7 = 5x - 6\],
we rearranged it by combining like terms and moved all \(x\) terms to one side.
The rearrangement yielded:\[7 = 6x - 6\].
By rearranging equations like this, we align terms logically, so solving becomes an easier task.
Finally, to solve for \(x\), divide both sides of the rearranged equation by the coefficient of \(x\), i.e., 6, leading us to:\[x = \frac{13}{6}\].
Equation rearrangement not only streamlines the process of isolation but also clarifies which operations to perform, making it a crucial part of linear equations.