To solve the inequality [tex]\( |3x - 3| \leq 18 \)[/tex], we need to break it down systematically. Here are the steps:
1. Understand Absolute Value Inequality: The inequality [tex]\( |A| \leq B \)[/tex] translates to [tex]\( -B \leq A \leq B \)[/tex].
2. Apply to Our Problem: Here, [tex]\( A = 3x - 3 \)[/tex] and [tex]\( B = 18 \)[/tex]. Thus, the inequality [tex]\( |3x - 3| \leq 18 \)[/tex] becomes [tex]\( -18 \leq 3x - 3 \leq 18 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
- First, we solve the left-hand side: [tex]\( -18 \leq 3x - 3 \)[/tex].
- Add 3 to both sides: [tex]\( -18 + 3 \leq 3x \)[/tex].
- Simplify: [tex]\( -15 \leq 3x \)[/tex].
- Divide by 3: [tex]\( -5 \leq x \)[/tex].
- Next, we solve the right-hand side: [tex]\( 3x - 3 \leq 18 \)[/tex].
- Add 3 to both sides: [tex]\( 3x \leq 18 + 3 \)[/tex].
- Simplify: [tex]\( 3x \leq 21 \)[/tex].
- Divide by 3: [tex]\( x \leq 7 \)[/tex].
4. Combine Results: We combine both results to get the final solution: [tex]\( -5 \leq x \leq 7 \)[/tex].
Therefore, the solution to the inequality [tex]\( |3x - 3| \leq 18 \)[/tex] is
[tex]\[ -5 \leq x \leq 7. \][/tex]
Hence, the correct answer is
[tex]\[ \boxed{-5 \leq x \leq 7.} \][/tex]
