How do you solve and graph #-6 <3x + 2 < 11#?

This can be plotted on a number line as shown in the Answer (above); notice the hollow circles which indicate the those values are not included in the solution.,

To solve and graph the inequality -6 < 3x + 2 < 11:

1. Subtract 2 from all parts of the inequality.
2. Divide all parts by 3.
3. Represent the solution on a number line.

To solve and graph the compound inequality ( -6 < 3x + 2 < 11 ):

1. Subtract 2 from all parts of the compound inequality:

[ -6 - 2 < 3x + 2 - 2 < 11 - 2 ]

This simplifies to:

[ -8 < 3x < 9 ]

2. Divide all parts of the compound inequality by 3:

[ \frac{-8}{3} < \frac{3x}{3} < \frac{9}{3} ]

This simplifies to:

[ \frac{-8}{3} < x < 3 ]

So, the solution to the compound inequality is ( \frac{-8}{3} < x < 3 ).

To graph this on a number line, plot an open circle at ( x = \frac{-8}{3} ) and at ( x = 3 ), indicating that the endpoints are not included in the solution. Then, shade the region between these two points, indicating that all values of ( x ) within this interval satisfy the compound inequality.