Question

solve the inequality. then graph the solution set on a number line.
2 < c + 5 ≤ 6
progress: 0/2
part 1 of 2
(a) solve the inequality 2 < c + 5 ≤ 6.

Explanation:

Step1: Subtract 5 from all parts

To solve the compound inequality \(2 < c + 5 \leq 6\), we subtract 5 from each part of the inequality. This is based on the property of inequalities that if we perform the same operation (subtraction of 5 here) on all parts of a compound inequality, the inequality signs remain the same. So we have:
\(2 - 5 < c + 5 - 5 \leq 6 - 5\)

Step2: Simplify each part

Simplify the left, middle, and right parts of the inequality.
For the left part: \(2 - 5=-3\)
For the middle part: \(c + 5 - 5 = c\)
For the right part: \(6 - 5 = 1\)
Putting it all together, we get \(-3 < c \leq 1\)

Answer:

\(-3 < c \leq 1\)