Question

What happened to the glass blower who inhaled?

Answer 1

The correct answers are:

#1) Graph I; #2) Graph O; #3) Graph C; #4) Graph E; #5) Graph N; #6) Graph G; #7) Graph M; #8) Graph H; #9) Graph T; #10) Graph S; #11) Graph P; #12) Graph A

He got a pane in his stomach.

Step-by-step explanation:

#1) We want a graph where -4 is circled and not filled in, and -1 is circled and filled in; from -4, the graph goes to the right and from -1 it goes to the left, meeting between the two numbers and not extending further. This is graph I.

#2) Solving the first inequality, we subtract 4 from each side; this gives us x > -1. Solving the second inequality, we add 2 to each side; this gives us x < 4. We want a graph where -1 is circled and not filled in, and 4 is circled and not filled in, with the line shaded between them. This is graph O.

#3) We want a graph where -2 is circled and filled in and 3 is circled and not filled in; from -2, the graph is shaded left and from 3 the graph is shaded right. This is graph C.

#4) Solving the first inequality, divide both sides by -3; this gives us t<-4 (remember we flip the symbol when we divide by a negative number). Solving the second inequality, divide both sides by 5; this gives us t≥2. We want a graph where -4 is circled and not filled in, and 2 is circled and filled in; from -4 the graph is shaded left and from 2 the graph is shaded right. This is graph E.

#5) Solving the first inequality, subtract 5 from each side; this gives us 2n > -4. Divide both sides by 2; this gives us n>-2. Solving the second inequality, subtract 4 from each side; this gives us 3n>3. Divide both sides by 3, and we have n>1. This is and; this means we want an inequality showing n>-2 and n>1. It has to be true for both numbers; this means we want a graph of n>1. We want the number 1 circled and not filled in, and the graph shaded to the right; this is graph N.

#6) Solving the first inequality, subtract 9 from each side; this gives us -4u>-8. Divide both sides by -4, giving us u<2. Solving the second inequality, add 13 to each side; this gives us 7u≤7. Divide both sides by 7; this gives us u≤1. We want a graph showing that u<2 and u≤1; this means we want to go from the smaller number, so we want a graph of u≤1. We want a graph where 1 is circled and filled in, and the line is shaded to the left; this is graph G.

#7) Solving the first inequality, subtract 20 from each side; this gives us 12≤3x, or 3x≥12. Divide both sides by 3 and we have x≥4. Solving the second inequality, subtract 1 from each side; this gives us 16>-8x, or -8x<16. Divide both sides by -8, and we have x>-2. We want a graph where 4 is circled and filled in and -2 is circled and not filled in; since this is "or" we include both answers. This means everything from -2 to the right is shaded; this is graph M.

#8) Solving the first inequality, subtract 8 from each side; this gives us -2k<6. Divide both sides by -2 and we have k>-3. Solving the second inequality, subtract 1 from each side; this gives us 3k<0. Divide both sides by 3 and we have k<0. We want a graph where -3 is circled and not filled in and 0 is circled and not filled in; this is "or" so we include both possibilities. Everything greater than -3 is shaded to the right and everything less than 0 is shaded to the left; this means everything is shaded, or graph H.

#9) Solving the first inequality, divide both sides by 5; this gives us w+4≥1. Subtract 4 from each side and we have w≥-3. Solving the second inequality, divide both sides by 2; this gives us w+4<6. Subtract 4 from each side and we have w<2. We want a graph where -3 is circled and filled in and 2 is circled and not filled in, with everything between them shaded; this is graph T.

#10) Solving the first inequality, divide both sides by 3; this gives us 6-y≤2. Subtract 6 from both sides; this gives us -y≤-4. Divide both sides by -1 and we have y≥4. Solving the second inequality, subtract 6 from both sides; this gives us -y≥2. Divide both sides by -1 and we have y≤-2. There is no way to graph everything that is larger than a positive and less than a negative at the same time, so this is graph S, the empty set.

#11) Solving the first inequality, subtract 2x from each side; this gives us x<-3. Solving the second inequality, subtract 4x from each side; this gives us 3x>-9. Divide both sides by 3 and we have x>-3. We want a graph where -3 is circled and not filled in, and everything on both sides is shaded; this is graph P.

#12) To solve first equation, multiply both sides by 2; this gives us x≤-4. To solve the second equation, multiply both sides by -2; this gives us x≤0. We want everything less than or equal to -4 or less than or equal to 0; this means we want everything smaller than 0, with 0 filled in. This is graph A.

Answer 2

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.