We are given compound inequality 4p + 1 > −7 or 6p + 3 < 33.
Let us solve each of the inequality one by one.
4p + 1 > −7
Subtracting 1 from both sides, we get
4p + 1-1 > -7-1
4p > -8
Dividing both sides by 4, we get
p > -2. <em> (Shading right side for greater than sign)</em>
Solving 6p + 3 < 33.
Subtracting 3 from both sides, we get
6p + 3-3 < 33-3.
6p < 30
Dividing both sides by 6, we get
p < 5. <em> (Shading left for less than sign)</em>
<em>We have less than and greater than symbols in both inequalities, therefore we would have open circles(dots) on -2 and 5.</em>
And because we have "OR" composite inequality.
<em>So, we would take the combination of both shaded portion.</em>
<h3>Therefore, correct option is C.number line with shading everywhere.. </h3>
