Let's analyze and complete the solution step-by-step for question 4 in your image.

Question 4: Solve $|6 - 3x| = 12$

The problem requires solving the equation and completing the explanation:

Step 1: Handling the absolute value

The expression inside absolute value bars can represent a positive or negative value. Thus: $6 - 3x = 12 \quad \text{or} \quad 6 - 3x = -12$

Step 2: Solve each equation separately

1. From the first equation $6 - 3x = 12$: Subtract 6 from both sides: $-3x = 12 - 6 \implies -3x = 6$ Divide by $-3$: $x = -2$

2. From the second equation $6 - 3x = -12$: Subtract 6 from both sides: $-3x = -12 - 6 \implies -3x = -18$ Divide by $-3$: $x = 6$

Step 3: Write the solution

The solutions are: $x = -2 \quad \text{or} \quad x = 6$

Completed Explanation Table:

Would you like me to assist with question 5 as well or clarify any step further?

Relative Questions

1. How do absolute value equations differ from regular linear equations in their solutions?
2. Why does $|a| = b$ lead to two equations $a = b$ and $a = -b$?
3. What happens if the absolute value equation equals a negative number (e.g., $|x| = -5$)?
4. How can you verify your solutions for absolute value equations?
5. How do absolute value equations apply to real-world contexts?

Tip:

Always double-check your solutions by substituting them back into the original equation.