To solve the inequality $2(x - 3) < 8$, follow these steps:

Step 1: Expand the inequality

Distribute the $2$ to terms inside the parentheses: $2x - 6 < 8$

Step 2: Isolate the variable term

Add $6$ to both sides to eliminate the constant term on the left-hand side: $2x < 14$

Step 3: Solve for $x$

Divide both sides by $2$ to isolate $x$: $x < 7$

Final Solution:

$x < 7$

This means the solution set includes all values of $x$ less than $7$.

Would you like further explanation or details about graphing the solution?
Here are 5 related questions to deepen understanding:

1. How would the solution change if the inequality were $2(x - 3) \leq 8$?
2. Can you represent this inequality solution on a number line?
3. How do you solve inequalities with fractions, e.g., $\frac{1}{3}(x - 6) < 2$?
4. What happens if the inequality sign is flipped, e.g., $2(x - 3) > 8$?
5. How does solving inequalities differ from solving equations?

Tip: When multiplying or dividing inequalities by a negative number, remember to flip the inequality sign!