Question

solve the inequality and graph the solution.
11k + 5 > -17
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
(number line from -5 to 5 with ticks at each integer)

Explanation:

Step1: Subtract 5 from both sides

To isolate the term with \( k \), we subtract 5 from both sides of the inequality \( 11k + 5 > -17 \). This gives us \( 11k + 5 - 5 > -17 - 5 \), which simplifies to \( 11k > -22 \).

Step2: Divide both sides by 11

Next, we divide both sides of the inequality \( 11k > -22 \) by 11 to solve for \( k \). So, \( \frac{11k}{11} > \frac{-22}{11} \), which simplifies to \( k > -2 \).

Answer:

The solution to the inequality \( 11k + 5 > -17 \) is \( k > -2 \). To graph this, we draw an open circle at \( -2 \) (since the inequality is strict, \( k \) is not equal to \( -2 \)) and shade the region to the right of \( -2 \) on the number line.