Subtract 8 from both sides to get constants on one side:
\( 3 - 8 > 3x + 8 - 8 \) \( -5 > 3x \)
Divide both sides by 3 to solve for \( x \):
Remember, when dividing or multiplying both sides of an inequality by a negative number, you must flip the inequality symbol. But we are dividing by a positive number (3), so the direction stays the same.
\[ \frac{-5}{3} > x \] or rewritten, \[ x < -\frac{5}{3} \] As a mixed number, \( -\frac{5}{3} = -1\frac{2}{3} \).
Conclusion: The solution is \( x < -1\frac{2}{3} \). This means any value of \( x \) that is less than \( -1\frac{2}{3} \) makes the original inequality true.
Why is this true? The process of solving the inequality is just like solving equations: you isolate \( x \) using addition, subtraction, and division. The key thing in inequalities is to only flip the symbol if you multiply or divide by a negative number. Here, all steps kept the direction of the inequality the same.
