Question

choose the best answer.

1. which is the graph of the solution set for ( p - 6 geq -11 )?

a. graph
b. graph
c. graph
d. graph

1. alex spent $5 on a ticket to the baseball game leaving him with at least $15. which inequality will find the least amount, ( a ), he had before he bought the ticket?

f. ( a - 5 geq 15 )
h. ( a + 5 > 15 )
g. ( a - 5 > 15 )
j. ( a + 5 geq 15 )

1. which inequality has the solution set, ( s = { \text{numbers greater than or equal to 9} } )?

a. ( -12 geq -4 + u - 17 )
b. ( 4 leq -2 + u - 3 )
c. ( -6 + u + 1 geq -4 )
d. ( -17 + u - 2 leq -28 )

1. which inequality has the solution set as graphed? graph

f. ( -4 + e - 2 < 14 )
g. ( -13 > -5 + e - 2 )
h. ( e - 6 + (-2) < -12 )
j. ( e - 5 - 3 > 12 )

1. which is the solution set of ( -8 + q - 13 < -9 )?

a. ( q < -13 )
c. ( q > 12 )
b. ( -13 < q )
d. ( 12 > q )

1. three is subtracted from both sides of the modeled inequality. which inequality results? model

f. ( 1 > -1 )
h. ( 0 < 1 )
g. ( 0 > -5 )
j. ( 1 > -4 )

1. tristan purchased 3 snacks for a total less than $10. a bag of pretzels cost $2 and a bottle of water cost $3. what is the most that the fruit cup, the third snack, could have cost?

a. $5.00
c. $4.00
b. $4.99
d. $3.99

1. which property of inequality is modeled? graphs

f. addition property of inequality
g. division property of inequality
h. multiplication property of inequality
j. subtraction property of inequality

1. which property of inequality is modeled? models

a. addition property of inequality
b. division property of inequality
c. multiplication property of inequality
d. subtraction property of inequality

Explanation:

Step1: Solve inequality for Q11

Solve $p - 6 \geq -11$:
Add 6 to both sides:
$p \geq -11 + 6$
$p \geq -5$
This matches option C's graph (closed dot at -5, arrow right).

Step2: Translate scenario for Q12

Initial amount $a$, minus $5$ leaves at least $15$:
$a - 5 \geq 15$, which is option F.

Step3: Solve each inequality for Q13

We need solution $u \geq 9$:

• Option C: $-6 + u + 1 \geq -4$

Simplify: $u - 5 \geq -4$
Add 5 to both sides: $u \geq 1$ (no)
Correction: Option A: $-12 \geq -4 + u -17$
Simplify right side: $u -21$
$-12 \geq u -21$
Add 21: $9 \geq u$ → no
Option B: $4 \leq -2 + u -3$ → $4 \leq u -5$ → $u \geq 9$ (matches).

Step4: Interpret graph for Q14

Graph: open dot at 20, arrow left → $e < 20$
Check option F: $-4 + e -2 <14$ → $e -6 <14$ → $e <20$ (matches).

Step5: Solve inequality for Q15

$-8 + q -13 < -9$
Simplify left: $q -21 < -9$
Add 21: $q < 12$, which is $12 > q$ (option D).

Step6: Model initial inequality for Q16

Model: left has 3 squares, right has 2 → $3 > 2$
Subtract 3 from both sides: $3-3 > 2-3$ → $0 > -5$ (option G).

Step7: Calculate max fruit cup cost Q17

Let $x$ = fruit cup cost. Total < 10:
$2 + 3 + x < 10$ → $5 + x <10$ → $x <5$
Max value is $4.99$ (option B, since it must be less than 5).

Step8: Identify inequality property Q18

Graph: start at $3 \leq 6$, subtract 5 from both sides: $3-5 \leq 6-5$ → $-2 \leq 1$, which uses Subtraction Property (option J).

Step9: Identify inequality property Q19

Model: left has 3, right has 0 → $3 > 0$. Add 2 to both sides: $3+2 >0+2$ → $5>2$, which uses Addition Property (option A).

Answer:

1. C
2. F. $a - 5 \geq 15$
3. B. $4 \leq -2 + u - 3$
4. F. $-4 + e - 2 < 14$
5. D. $12 > q$
6. G. $0 > -5$
7. B. $\$4.99$
8. J. Subtraction Property of Inequality
9. A. Addition Property of Inequality