A fence company has 100 meters of fencing material. They want to build a rectangular vegetable garden with a walkway around it. The walkway will have a uniform width of 1 meter along all sides of the garden. Let x be the length (in meters) and y be the garden’s width (in meters). Write down a system of inequalities to represent the constraints.

A) ​\$ ("x" + 2) + 2("y" + 2) ≤ 100, "x" ≥ 0, "y" ≥ 0 \$​

B) ​\$ ("x" + 2) + ("y" + 2) ≤ 100, "x" ≥ 0, "y" ≥ 0 \$​

C) ​\$ 2("x" + 2) + 2("y" + 2) ≤ 100, "x" ≥ 0, "y" ≥ 0 \$​

D) ​\$ 2("x" + 2) + 2("y" + 2) ≤ 100, "x" ≤ 0, "y" ≤ 0 \$​

Solve the following system of inequalities: \$x/(2"x" + 1) ≥ 1/4\$, \$(6"x")/(4"x" - 1) < 1/2\$

A) 0

B) Solutions

C) Infinity

D) No solution

The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realize some profit?

A) x ≠ 50

B) x > 50

C) x = 50

D) x < 50

The population of the town in 2020 was 100000. The population decreased by y% from 2020 to 2021 and increased by x% from 2021 to 2022, where x and y are two natural numbers. If the population in 2022 was greater than the population in 2020 and the difference between x and y is 10, then the lowest possible population of the town in 2021 was.

A) 73000

B) 74000

C) 71000

D) 75000

In drilling the world’s deepest hole, it was found that the temperature T in degrees Celsius, x km below the earth’s surface, was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?

A) 8 < x < 10

B) 8 > x < 10

C) 8 > x > 10

D) 8 < x > 10

A company sells two types of products, X and Y. Each unit of product X contributes $5 to profit, while each unit of product Y contributes $8. If the company needs to make at least $1000 in profit and can sell at most 200 units of product X and 150 units of product Y, write and solve a system of inequalities to represent the possible combinations of products the company can sell to achieve its profit goal.

A) \$ 5"x" + 8"y" ≥ 100, "x" ≤ 200, "y" ≤ 150, "x" ≥ 0, "y" ≥ 0 \$

B) \$ 5"x" + 8"y" ≥ 1000, "x" ≤ 200, "y" ≤ 150, "x" ≥ 0, "y" ≥ 0 \$ ​

C) \$ 5"x" + 8"y" ≥ 1000, "x" ≤ 100, "y" ≤ 250, "x" ≥ 0, "y" ≥ 0 \$

D) \$ 5"x" + 8"y" ≥ 10, "x" ≤ 20, "y" ≤ 15, "x" ≥ 0, "y" ≥ 0 \$

Solve the inequality and represent the solution set:
\$ 3"x"^2 − 7"x" + 2 < 0 \$

A) \$ (4/3​, 2) \$

B) \$ (1/3​, 2) \$

C) \$ (2/3​, 1) \$

D) \$ (7/3​, 1) \$

Solve the inequality:
\$ \∣4"x" − 5\∣ − \∣ 2"x" + 3\∣ ≤ 1 \$

A) \$(1/2), (9/4)​\$

B) \$ (1​/6), (7/2)​\$

C) \$ (1​/6), (9/2)​\$

D) \$ (1​/6), (1/2)​\$

Solve the inequality and represent the solution set:
\$ ("x"^2 − 4"x" + 3 ​≥ 0)/("x" + 1) \$

A) \$ "x" ∈ (−1, 1) ∪ (2, ∞) \$

B) \$ x ∈ (−1, 2) ∪ (3, ∞) \$

C) \$ x ∈ (−1, 1) ∪ (3, ∞) \$

D) \$ x ∈ (−2, 1) ∪ (-3, ∞) \$

Solve the inequality:
\$ ((2x − 1)/(x + 2))​ < ((x + 3)/(2x − 5)) \$

A) \$ (−∞, −4) ∪ (−2, −1/6​)\$

B) \$ (−∞, −2) ∪ (−2, −7/6​)\$

C) \$ (−∞, −3) ∪ (−1, −7/6​)\$

D) \$ (−∞, −3) ∪ (−2, −7/6​)\$