Question

choose the best answer.

1. which is the solution set, s, for

$ -16 < x + 4 $?
a. $ s = \\{ \text{numbers greater than } -20 \\} $
b. $ s = \\{ \text{numbers less than } -20 \\} $
c. $ s = \\{ \text{numbers greater than } -12 \\} $
d. $ s = \\{ \text{numbers less than } -12 \\} $

1. which inequality has a solution of $ a < 15 $?

f. $ a + 4 < -11 $
g. $ 10 < a + 25 $
h. $ 12 + a > 3 $
j. $ 22 > a + 7 $

1. which is the graph of the solution set

for $ y + 18 \geq 11 $?
a. graph
b. graph
c. graph
d. graph

1. which is the solution of $ 14 + n - 6 \leq 10 $?

f. $ n \leq -2 $
g. $ n \leq 2 $
h. $ n \leq 8 $
j. $ n \leq 18 $

1. which inequality has the solution set,

$ s = \\{ \text{numbers less than } -4 \\} $?
a. $ 8 + c + (-6) > 2 $
b. $ -2 > 3 + c - 1 $
c. $ 14 > 6 + c + 4 $
d. $ -5 + c + 7 < 6 $

1. which inequality has a solution set as

graphed?
graph
f. $ 8 \leq -9 + b + 12 $
g. $ 10 + b - 6 \geq -1 $
h. $ -4 + b + 8 \geq 1 $
j. $ 4 \leq -1 + b + 10 $

1. which inequality has a solution set of $ z < 7 $?

a. $ -4 > 3 + z $
b. $ 2 + z + (-6) > 3 $
c. $ 3 < z - 4 $
d. $ -2 + z - 1 < 4 $

1. which inequality has a solution set as

graphed?
graph
f. $ w - 16 < 18 $
g. $ -4 + w - 2 < -8 $
h. $ 6 > 4 + w $
j. $ -1 < 1 + w $

1. which is the solution set, s, for $ -8 < m - 4 $?

a. $ s = \\{ \text{numbers less than } 12 \\} $
b. $ s = \\{ \text{numbers greater than } 12 \\} $
c. $ s = \\{ \text{numbers less than } -4 \\} $
d. $ s = \\{ \text{numbers greater than } -4 \\} $

1. which inequality has a solution

of $ r < 3 $?
f. $ 4 > r - 7 $
g. $ r - 6 > 9 $
h. $ r - 10 < -7 $
j. $ -5 < r - 2 $

Explanation:

Step1: Solve inequality 1

$-16 < x + 4$
Subtract 4 from both sides:
$x > -16 - 4$
$x > -20$

Step2: Solve inequality 2

Find option with $a < 15$:

• F: $a + 4 < -11 \implies a < -15$
• G: $10 < a + 25 \implies a > -15$
• H: $12 + a > 3 \implies a > -9$
• J: $22 > a + 7 \implies a < 15$

Step3: Solve inequality 3

$y + 18 \geq 11$
Subtract 18 from both sides:
$y \geq 11 - 18$
$y \geq -7$
Match to graph C.

Step4: Solve inequality 4

$14 + n - 6 \leq 10$
Simplify left side:
$8 + n \leq 10$
Subtract 8:
$n \leq 2$

Step5: Solve inequality 5

Find option with $c < -4$:

• A: $8 + c -6 > 2 \implies c > 0$
• B: $-2 > 3 + c -1 \implies -2 > c + 2 \implies c < -4$
• C: $14 > 6 + c + 4 \implies 14 > c + 10 \implies c < 4$
• D: $-5 + c + 7 < 6 \implies c + 2 < 6 \implies c < 4$

Step6: Solve inequality 6

Graph shows $b \geq 5$:

• F: $8 \leq -9 + b + 12 \implies 8 \leq b + 3 \implies b \geq 5$
• G: $10 + b -6 \geq -1 \implies b + 4 \geq -1 \implies b \geq -5$
• H: $-4 + b + 8 \geq 1 \implies b + 4 \geq 1 \implies b \geq -3$
• J: $4 \leq -1 + b + 10 \implies 4 \leq b + 9 \implies b \geq -5$

Step7: Solve inequality 7

Find option with $z < 7$:

• A: $-4 > 3 + z \implies z < -7$
• B: $2 + z -6 > 3 \implies z -4 > 3 \implies z > 7$
• C: $3 < z -4 \implies z > 7$
• D: $-2 + z -1 < 4 \implies z -3 < 4 \implies z < 7$

Step8: Solve inequality 8

Graph shows $w < -2$:

• F: $w -16 < 18 \implies w < 34$
• G: $-4 + w -2 < -8 \implies w -6 < -8 \implies w < -2$
• H: $6 > 4 + w \implies w < 2$
• J: $-1 < 1 + w \implies w > -2$

Step9: Solve inequality 9

$-8 < m - 4$
Add 4 to both sides:
$m > -8 + 4$
$m > -4$

Step10: Solve inequality 10

Find option with $r < 3$:

• F: $4 > r -7 \implies r < 11$
• G: $r -6 > 9 \implies r > 15$
• H: $r -10 < -7 \implies r < 3$
• J: $-5 < r -2 \implies r > -3$

Answer:

1. A. $S = \{\text{numbers greater than } -20\}$
2. J. $22 > a + 7$
3. C. (Graph with closed dot at -7, arrow right)
4. G. $n \leq 2$
5. B. $-2 > 3 + c -1$
6. F. $8 \leq -9 + b + 12$
7. D. $-2 + z -1 < 4$
8. G. $-4 + w -2 < -8$
9. D. $S = \{\text{numbers greater than } -4\}$
10. H. $r - 10 < -7$