91Ó°ÊÓ

Isolating the variable term is a crucial first step in solving linear equations. The goal is to get all the terms containing the variable on one side of the equation. In our example, we start with:
$$ \frac{2}{9} x + \frac{5}{3} = \frac{5}{9} x + \frac{7}{3} $$
To isolate the variable term, we subtract \(\frac{5}{9} x\) from both sides. This leaves all the x terms on one side and the constants on the other side:
\[ \frac{2}{9} x - \frac{5}{9} x + \frac{5}{3} = \frac{7}{3} \]
Perform the subtraction:
\[ -\frac{3}{9} x + \frac{5}{3} = \frac{7}{3} \]
Which simplifies further to:
\[ -\frac{1}{3} x + \frac{5}{3} = \frac{7}{3} \]
With all x terms on one side, we're ready for the next step.

Simplifying equations helps make them more manageable to solve. Once the variable terms are isolated, we need to simplify by removing constants from the variable side. For our equation, we have:
\[ -\frac{1}{3} x + \frac{5}{3} = \frac{7}{3} \]
To eliminate the \(\frac{5}{3}\) term, subtract \(\frac{5}{3}\) from both sides:
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