Question

e the linear inequality for k and graph the answer in the number line. then write the solution in inequality notation.
$k + 1 < -2$
/ your work here
to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Subtract 1 from both sides

To solve the inequality \( k + 1 < -2 \), we subtract 1 from both sides of the inequality. This is based on the property of inequalities that allows us to add or subtract the same number from both sides without changing the direction of the inequality.
\[
k + 1 - 1 < -2 - 1
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( k+1 - 1=k \). Simplifying the right - hand side, \( - 2-1=-3 \). So we get:
\[
k < - 3
\]

Answer:

The solution to the inequality \( k + 1 < -2 \) is \( k < - 3 \). To graph this on the number line, we would place an open circle at \( - 3 \) (since \( k\) is not equal to \( - 3\)) and draw an arrow to the left of \( - 3 \) to represent all numbers less than \( - 3 \). The inequality notation for the solution is \( k < - 3 \).