Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Ask anything and receive well-informed answers from our community of experienced professionals.

Question 2 (Multiple Choice, Worth 5 points)

What is the solution to [tex]4|x-6| \leq 16[/tex]?

A. [tex]x \leq 2[/tex] or [tex]x \geq 10[/tex]

B. [tex]2 \leq x \leq 10[/tex]

C. [tex]-10 \leq x \leq 2[/tex]

D. [tex]x \leq -10[/tex] or [tex]x \geq 2[/tex]


Sagot :

To find the solution to the inequality [tex]\(4|x - 6| \leq 16\)[/tex]:

1. First, isolate the absolute term by dividing both sides by 4:
[tex]\[ |x - 6| \leq 4 \][/tex]

2. This inequality means that the expression inside the absolute value, [tex]\(x - 6\)[/tex], can vary between -4 and 4, inclusive. Therefore, we can write the compound inequality:
[tex]\[ -4 \leq x - 6 \leq 4 \][/tex]

3. Next, solve this compound inequality step-by-step:

a. Add 6 to all parts of the inequality to isolate [tex]\(x\)[/tex]:
[tex]\[ -4 + 6 \leq x - 6 + 6 \leq 4 + 6 \][/tex]

b. Simplify the resulting expression:
[tex]\[ 2 \leq x \leq 10 \][/tex]

So, the solution to the inequality [tex]\(4|x - 6| \leq 16\)[/tex] is:
[tex]\[ 2 \leq x \leq 10 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{2 \leq x \leq 10} \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.