Question

solve for c and graph the solution.
|c + 2| < 1
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or
two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles,
click on them.
submit

Explanation:

Step1: Solve the inequality

For \(|c + 2|\lt1\), we know that if \(|x|\lt a\) (\(a\gt0\)), then \(-a\lt x\lt a\). Here \(x = c + 2\) and \(a = 1\). So we have \(-1\lt c+2\lt1\).
Subtract 2 from all parts of the compound - inequality: \(-1-2\lt c+2 - 2\lt1 - 2\).
Which simplifies to \(-3\lt c\lt - 1\).

Step2: Graph the solution

The solution \(c\) is all real numbers between \(-3\) and \(-1\). On the number - line, we use open circles at \(c=-3\) and \(c = - 1\) (because the inequality is strict, i.e., \(c
eq-3\) and \(c
eq-1\)) and draw a line segment between them.

Answer:

The solution of the inequality \(|c + 2|\lt1\) is \(-3\lt c\lt - 1\). On the number - line, we have open circles at \(c=-3\) and \(c=-1\) with a line segment connecting them.