Question

solve for c.
|c - 1| ≤ 3
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. use integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Remove absolute - value

We know that if \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\). So for \(|c - 1|\leq3\), we have \(-3\leq c - 1\leq3\).

Step2: Solve for \(c\)

Add 1 to all parts of the compound - inequality. \(-3+1\leq c-1 + 1\leq3 + 1\).
This simplifies to \(-2\leq c\leq4\).

Answer:

\(-2\leq c\leq4\)