1

A company produces two types of smartphones, A and B. The profit per unit of smartphone A is $50, and for smartphone B is $70. The company wants to maximize its profit while producing no more than 2000 units of smartphones. Let x represent the number of units of smartphone A and y represent the number of units of smartphone B. Writes and solve a system of inequalities to represent this situation.

A) x = 0, y = 2000

B) x = 0, y = 2999

C) x = 1, y = 1998

D) x = 1, y = 2001

2

Solve the inequality:
\$ ∣4x − 13∣ < 52 \$

A) \$ −33​/4 < x < 61/4 \$​

B) \$ −31​/4 < x < 65/4 \$​

C) \$ −39​/4 < x < 61/4 \$​

D) \$ −39​/4 < x < 65/4 \$​

3

A store sells apples for $0.50 each and oranges for $0.75 each. A customer wants to buy at most 10 fruits and spend at most $6. Write and solve a system of inequalities to represent this situation.

A) \$ 0.52x + 0.75y ≤ 6, x + y ≤ 10 \$​

B) \$ 0.50x + 0.75y ≤ 6, x + y ≤ 10 \$​

C) \$ 0.50x + 0.75y ≤ 6, x + y ≤ 15 \$​

D) \$ 0.50x + 0.15y ≤ 4, x + y ≤ 12 \$​

4

A car rental agency charges $30 per day for a compact car and $50 per day for a luxury car. A customer wants to rent cars for at most 7 days, and the total rental cost should not exceed $250. Let x represent the number of days a compact car is rented and y represent the number of days a luxury car is rented. Write and solve a system of inequalities to represent this situation.

A) \$ 5 ≤ x ≤ 7 \$ and \$ y ≤ 1 \$

B) \$ 2 ≤ x ≤ 7 \$ and \$ y ≤ 2 \$

C) \$ 5 ≤ x ≤ 7 \$ and \$ y ≤ 2 \$

D) \$ 5 ≤ x ≤ 6 \$ and \$ y ≤ 4 \$

5

Solve the inequality:
\$ ((x−2​)/3) ≥ ((x/2) ​− 1) \$​

A) \$ x ≤ 4 \$

B) \$ x ≤ 1 \$

C) \$ x ≤ 3 \$

D) \$ x ≤ 2 \$

6

Solve the absolute value inequality:
\$ ∣x − 14∣ ≤ 2 \$

A) \$ 10 ≤ x ≤ 16 \$

B) \$ 12 ≤ x ≤ 14 \$

C) \$ 12 ≤ x ≤ 16 \$

D) \$ 10 ≤ x ≤ 14 \$

7

In a triangle, the lengths of the sides are represented by a, b, and c. If a + b > c, b + c > a, and a + c > b, then the triangle is valid. Given a = 3x − 2, b = x + 4, and c = 2x + 1, find the range of values of x for which the triangle is valid.

A) \$ x > 5​/4 \$

B) \$ x > 1/4 \$

C) \$ x > 3​/4 \$

D) \$ x > 7​/4 \$

8

A rectangle has a length that is three times its width. If the perimeter of the rectangle is less than or equal to 40 meters, write and solve a system of inequalities to represent the possible dimensions of the rectangle.

A) ​\$ l = 2w, w ≤ 5, w ≥ 0 \$​

B) ​​\$ l = 3w, w ≤ 5, w ≥ 0 \$​

C) ​\$ l = 3w, w ≤ 4, w ≥ 0 \$

D) ​\$ l = 4w, w ≤ 3, w ≥ 1 \$​

9

Solve the inequality:
\$ (2x−1) / (x + 3) > 1 \$

A) \$ x ∈ (−∞,−1) ∪ (4,∞) \$

B) \$ x ∈ (−∞,−3) ∪ (2,∞) \$

C) \$ x ∈ (−∞,−3) ∪ (4,∞) \$

D) \$ x ∈ (−∞,−2) ∪ (3,∞) \$

10

A charity organization is planning a fundraising event. They can sell tickets for $10 each for adults and $5 each for children. They want to sell at least 200 tickets and earn at least $1500. Let x represent the number of adult tickets sold and y represent the number of children’s tickets sold. Write and solve a system of inequalities to represent this situation.

A) \$ x ≥ 100 and y ≤ 100 \$

B) \$ x ≥ 200 and y ≤ 200 \$

C) \$ x ≥ 200 and y ≤ 100 \$

D) \$ x ≥ 200 and y ≤ 100 \$