Read the following plan for a study Draw any conclusions about how the statistics produced could be misleading
Tony is a high school math teacher. He wants to do a study on what his previous math students have been doing since
they graduated high school. He made a survey with questions like, "What year did you graduate high school?" and
"What was your major in college?" He used the student home addresses on file with the guidance office to send the
surveys. He included a return envelope with the school address so that the surveys would remain anonymous

From the attachment, the solution set of each combined ineaquality are as follows:

Part 1:

For 1,
The solution set for x > -4  and x ≤ -1 is the number line labeled I.

Part 2:

For 2,
x + 5 > 4 and x - 2 < 2
x + 5 - 5 > 4 - 5 and x - 2 + 2 < 2 + 2
x > -1 and x < 4
The solution set is the number line labelled O

Part 3:

For 3,
The solution set for y ≤ -2 or y > 3 is the number line labelled O.

Part 4:

For 4,
-3t > 12 or 5t ≥ 10
-3t / -3 < 12 / -3 or 5t /5 ≥ 10 / 5         [note that when you divide an ineduality term by a negative number the inequality sign changes]
t < -4 or t ≥ 2
The solution set is the number line labelled E.

Part 5:
2n + 5 > 1 and 3n + 4 > 7
2n + 5 - 5 > 1 - 5 and 3n + 4 - 4 > 7 - 4
2n > -4 and 3n > 3
2n / 2 > -4 / 2 and 3n / 3 > 3 / 3
n > -2 and n > 1

The solution set is the number line labelled N.

Part 6:

For 6,
-4u + 9 > 1 and 7u - 13 ≤ -6
-4u + 9 - 9 > 1 - 9 and 7u - 13 + 13 ≤ -6 + 13
-4u > -8 and 7u ≤ 7
-4u / -4 < -8 / -4 and 7u / 7 ≤ 7 / 7
u < 2 and u ≤ 1

The solution set is the number line labelled G.

Part 7:

For 7,
32 ≤ 3x + 20 or 17 > 1 - 8x
32 - 20 ≤ 3x + 20 - 20 or 17 - 1 > 1 - 8x - 1
12 ≤ 3x or 16 > -8x
12 / 3 ≤ 3x / 3 or 16 / -8 < -8x / -8
4 ≤ x or -2 < x

The solution set is the number line labelled M.

Part 8:

For 8,
-2k + 8 < 14 or 3k + 1 < 1
-2k + 8 - 8 < 14 - 8 or 3k + 1 - 1 < 1 - 1
-2k < 6 or 3k < 0
-2k / -2 > 6 / -2 or 3k / 3 < 0 / 3
k > -3 or k < 0.

The solution set is the number line labelled H.

Part 9:

For 9,
5(w + 4) ≥ 5  and 2(w + 4) < 12
5(w + 4) / 5 ≥ 5 / 5 and 2(w + 4) < 12 / 2
w + 4 ≥ 1 and w + 4 < 6
w + 4 - 4 ≥ 1 - 4 and w + 4 - 4 < 6 - 4
w ≥ -3 and w < 2

The solution set is the number line labelled T.

Part 10:

For 10,
3(6 - y) ≤ 6 and 6 - y ≥ 8
3(6 - y) / 3 ≤ 6 / 3 and 6 - y ≥ 8
6 - y ≤ 2 and 6 - y ≥ 8
6 - y - 6 ≤ 2 - 6 and 6 - y - 6 ≥ 8 - 6
-y ≤ -4 and -y ≥ 2
-y / -1 ≥ -4 / -1 and -y / -1 ≤ 2 / -1
y ≥ 4 and y ≤ -2

Because there is no number that is greater that 4 and at the same time less than -2. The solution set is empty.
Thus the solution set is labelled S.

Part 11:

For 11,
3x < 2x - 3 or 7x > 4x - 9
3x - 2x < 2x - 3 - 2x or 7x - 4x > 4x - 9 - 4x
x < -3 or 3x > -9
x < -3 or 3x / 3 > -9 / 3
x < -3 or x > -3

The solution set is the number line labelled P.

Part 12:

For 12,
x / 2 ≤ -2 or -x / 2 ≥ 0
2(x / 2) ≤ 2(-2) or 2(-x / 2) ≥ 2(0)
x ≤ -4 or -x ≥ 0
x ≤ -4 or -x / -1 ≤ 0 / -1
x ≤ -4 or x ≤ 0

The solution set is the number line labelled A.