Write the solution to −9+4|x−1|≤7 as a compound inequality.(1 point) Responses x≤−3 or x≥5 x less-than-or-equal-to negative 3 or x greater-than-or-equal-to 5 −3≤x≤5 negative 3 less-than-or-equal-to x less-than-or-equal-to 5 x≤3 x less-than-or-equal-to 3 no solution

Answer 1

To solve the inequality \(-9 + 4|x - 1| \leq 7\), we can start by isolating the absolute value term.

1. Add 9 to both sides:

   \[ 4|x - 1| \leq 16 \]

2. Divide both sides by 4:

   \[ |x - 1| \leq 4 \]

Now, we can interpret this absolute value inequality. The expression \(|x - 1| \leq 4\) translates to the compound inequality:

\[ -4 \leq x - 1 \leq 4 \]

3. Next, we will solve for \(x\) by adding 1 to all parts of the inequality:

   \[ -4 + 1 \leq x - 1 + 1 \leq 4 + 1 \]

   This simplifies to:

   \[ -3 \leq x \leq 5 \]

Thus, the solution to the inequality \(-9 + 4|x - 1| \leq 7\) is:

\[ -3 \leq x \leq 5 \]

The correct response from the options provided is:

−3 ≤ x ≤ 5