Question

Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33?. . A.a number line with open circles at -2 and 5 with shading in between.. . B.number line with open dots at ¨C2 and 5 and shading to the right of 5 and to the left of ¨C2.. . C.number line with shading everywhere.. . D.number line with open dot at ¨C2 and a closed dot at 5 and shading in between.

Answer 1

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. (Shading right side for greater than sign)

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. (Shading left for less than sign)

We have less than and greater than symbols in both inequalities, therefore we would have open circles(dots) on -2 and 5.

And because we have "OR" composite inequality.

So, we would take the combination of both shaded portion.

Therefore, correct option is C.number line with shading everywhere..