Check validity: For $ x = 2 $, $ |2 - 3| = 1 $ and $ 2(2) - 5 = -1 $. Not valid since LHS ≠ RHS. For $ x = \frac{8}{3} $, $ \left|\frac{8}{3} - 3\right| = \frac{1}{3} $ and $ 2\left(\frac{8}{3}\right) - 5 = \frac{1}{3} $. Valid.

["Check Validity: When expressions match — A math validation example with $ x = 2 $ and $ x = \frac{8}{3} $", "When solving equations or verifying expressions, a critical step is checking whether both sides of an equation are equal for a given value of $ x $. This process of validity checking ensures mathematical accuracy and prevents errors in reasoning. Let’s explore two concrete examples to understand how to assess validity in algebra.", "---", "### Example 1: Invalid Validation at $ x = 2 $", "Consider the equation:\n$$\n|2 - 3| = 2(2) - 5\n$$\nSubstituting $ x = 2 $:", "- Left-hand side (LHS):\n$$\n|2 - 3| = |-1| = 1\n$$\n- Right-hand side (RHS):\n$$\n2(2) - 5 = 4 - 5 = -1\n$$", "Since $ 1 <br/>\ne -1 $, the expressions are not valid for $ x = 2 $. This discrepancy shows that $ x = 2 $ is not a solution, and the equation fails to hold.", "Why check validity?\nValidation confirms whether a value satisfies a given equation. If not, we know the candidate for a solution is incorrect — crucial when solving linear, absolute value, or rational expressions.", "---", "### Example 2: Valid Validation at $ x = \frac{8}{3} $", "Now test $ x = \frac{8}{3} $:", "- LHS:\n$$\n\left| \frac{8}{3} - 3 \right| = \left| \frac{8}{3} - \frac{9}{3} \right| = \left| -\frac{1}{3} \right| = \frac{1}{3}\n$$\n- RHS:\n$$\n2\left( \frac{8}{3} \right) - 5 = \frac{16}{3} - \frac{15}{3} = \frac{1}{3}\n$$", "Both sides equal $ \frac{1}{3} $, so the expressions are valid at $ x = \frac{8}{3} $. This confirms $ x = \frac{8}{3} $ is a correct solution.", "---", "### Conclusion: Validity Confirms Solutions", "Checking validity by substituting values into both sides of an equation is a fundamental skill in algebra. As seen:", "- $ x = 2 $ fails due to $ |2 - 3| <br/>\ne 2(2) - 5 $\n- $ x = \frac{8}{3} $ satisfies $ \left| \frac{8}{3} - 3 \right| = 2\left( \frac{8}{3} \right) - 5 $", "Always verify both sides before declaring a value valid. This practice strengthens problem-solving accuracy and prevents misinterpretations in mathematical reasoning.", "For further understanding, explore different expressions and test various values to reinforce your validation skills!", "---", "Key takeaways:**\n- Validity means both sides of an equation are equal for a given $ x $.\n- Always substitute values to confirm solutions.\n- Discrepancies signal errors or that $ x $ is not a solution.", "Mastering validity checks ensures accuracy in algebra and builds confidence in solving equations."]