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 = 1, y = 1998

B) x = 0, y = 2999

C) x = 0, y = 2000

D) x = 1, y = 2001

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) \$

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 \$

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 ≤ 2 \$

B) \$ 2 ≤ x ≤ 7 \$ and \$ y ≤ 2 \$

C) \$ 5 ≤ x ≤ 7 \$ and \$ y ≤ 1 \$

D) \$ 5 ≤ x ≤ 6 \$ and \$ y ≤ 4 \$

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

A) \$ x ≤ 2 \$

B) \$ x ≤ 1 \$

C) \$ x ≤ 3 \$

D) \$ x ≤ 4 \$

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

A) \$ 10 ≤ x ≤ 16 \$

B) \$ 12 ≤ x ≤ 16 \$

C) \$ 12 ≤ x ≤ 14 \$

D) \$ 10 ≤ x ≤ 14 \$

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" > (1/4) \$

B) \$ x > (5​/4) \$

C) \$ x > (3​/4) \$

D) \$ x > (7​/4) \$

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" = 2"w", "w" ≤ 5, "w" ≥ 0 \$

B) ​\$ "l" = 3"w", "w" ≤ 4, "w" ≥ 0 \$

C) ​\$ "l" = 3"w", "w" ≤ 5, "w" ≥ 0 \$

D) ​\$ "l" = 4"w", "w" ≤ 3, "w" ≥ 1 \$

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

A) \$ x ∈ (−∞, −1) ∪ (4, ∞) \$

B) \$ x ∈ (−∞, −3) ∪ (2, ∞) \$

C) \$ x ∈ (−∞, −3) ∪ (4, ∞) \$

D) \$ x ∈ (−∞, −2) ∪ (3, ∞) \$

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" ≥ 200\$ and \$"y" ≤ 100 \$

B) \$ "x" ≥ 200\$ and \$"y" ≤ 200 \$

C) \$ "x" ≥ 200\$ and \$"y" ≤ 100 \$

D) \$ "x" ≥ 100\$ and \$"y" ≤ 100 \$