Question

solve the inequality and graph the solution.
6c + 9 < 3
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.
<----|----|----|----|----|----|----|----|----|----|--->
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \( c \), we subtract 9 from both sides of the inequality \( 6c + 9 < 3 \). This gives us \( 6c + 9 - 9 < 3 - 9 \), which simplifies to \( 6c < -6 \).

Step2: Divide both sides by 6

To solve for \( c \), we divide both sides of the inequality \( 6c < -6 \) by 6. So, \( \frac{6c}{6} < \frac{-6}{6} \), which simplifies to \( c < -1 \).

Answer:

The solution to the inequality \( 6c + 9 < 3 \) is \( c < -1 \). To graph this, we place an open circle at \( -1 \) (since the inequality is strict, \( c \) is not equal to \( -1 \)) and draw a ray to the left of \( -1 \) on the number line.