Problem

Solve |x−8|≤4

Answer

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Answer

Final Answer: The solution to the inequality |x−8|≤4 is [4,12].

Steps

Step 1 ：The absolute value of a number is its distance from zero on the number line. Therefore, the inequality |x−8|≤4 means that the distance between x and 8 on the number line is less than or equal to 4. This can be solved by setting up two inequalities: x−8≤4 and −(x−8)≤4.

Step 2 ：Solving these inequalities gives us the solutions x=12 and x=4. However, these are the endpoints of the interval of solutions.

Step 3 ：The solution to the original inequality |x−8|≤4 is the interval [4,12].

Step 4 ：Final Answer: The solution to the inequality |x−8|≤4 is [4,12].

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