Solve the inequality involving absolute value. Write your final answer in interval notation. (If the solution set is empty, enter EMPTY or $\emptyset$.)
\[
|-2 x+3| \leq 17
\]
Answer
Final Answer: The solution to the inequality \(|-2x+3| \leq 17\) is \(\boxed{[-7, 10]}\).
Step 1 ：The absolute value of a number is its distance from zero on the number line. Therefore, the inequality \(|-2x+3| \leq 17\) means that the distance between \(-2x+3\) and 0 is less than or equal to 17. This can be rewritten as two separate inequalities: \(-17 \leq -2x+3 \leq 17\).
Step 2 ：Solving these inequalities gives the solutions \(x = -7\) and \(x = 10\).
Step 3 ：This means that the solution to the original inequality is the interval \([-7, 10]\).
Step 4 ：Final Answer: The solution to the inequality \(|-2x+3| \leq 17\) is \(\boxed{[-7, 10]}\).
