1.2 The solution to the absolute value inequality $$ |x-6| \leqslant 2 $$ is: a) $$ x \in(-\infty, 8] $$ b) $$ x \in[4,8] $$ c) $$ x \in(-\infty, 4] \cup[8, \infty) $$ d) $$ x \in(-\infty,-2] $$ e) None of the above

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UpStudy AI · Accepted Answer

1. Write the absolute value inequality:

$$
|x-6| \leq 2
$$

2. By the definition of absolute value inequalities, this inequality can be rewritten as a compound inequality:

$$
-2 \leq x-6 \leq 2
$$

3. Add $$6$$ to all three parts of the inequality to isolate $$x$$:

$$
-2 + 6 \leq x-6 + 6 \leq 2 + 6
$$

Which simplifies to:

$$
4 \leq x \leq 8
$$

4. Therefore, the solution set is:

$$
x \in [4,8]
$$

Thus, the correct answer is option b.
The solution to the inequality $$ |x-6| \leq 2 $$ is $$ x \in [4,8] $$.

1.2 The solution to the absolute value inequality is:
a)
b)
c)
d)
e) None of the above

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1.2 The solution to the absolute value inequality is: a) b) c) d) e) None of the above