y ≤ x + 7 and y ≥ - 2x - 1
Which point (x, y) is a solution to the given system of inequalities in the xy-plane?

A) (-14, 0)

B) (0, 14)

C) (14, 0)

D) (0, -14)

A small business owner budgets $2,200 to purchase candles. The owner must buy at least 200 candles to maintain the discounted pricing. Suppose the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles. What is the maximum number of large candles the owner can buy to stay within the budget and maintain the discounted pricing?

A) 125

B) 128

C) 152

D) 182

If \$a + b = 2m^2\$, b + c = 6m, a + c = 2, where m is the real number and a ≤ b ≤ c, then which one of the following is correct?

A) \$0 ≤ "m" ≤ 1/2\$

B) \$1/3 ≤ "m" ≤ 1\$

C) -1 ≤ m ≤ 0

D) None of the above

y < 6x + 2
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

A)

B)

C)

D)

A classroom can fit at least 9 tables with an area of a one-meter square. We know that the perimeter of the classroom is 12m. Find the bounds on the length and breadth of the classroom.

A) L < 3 and B > 3

B) L = 3 and B = 3

C) L > 3 and B < 3

D) 0

Solve the compound inequality:
\$ −2 < 3 − 4"x" ≤ 7 \$

A) \$ (−2, 5/4​) \$

B) \$ (−1, 5/4​) \$

C) \$ (−1, 5/7) \$

D) \$ (−3, 5/2​) \$

A company needs to produce at least 100 units of product A and at least 150 units of product B. Product A requires 2 hours of labor per unit, and product B requires 3 hours per unit. The company has a total of 900 hours of labor available. Write down a system of inequalities to represent this situation.

A) \$ "x" ≤ 100, "y" ≥ 150, 2"x" + 3"y" ≤ 900​ \$

B) \$ "x" ≥ 100, "y" ≥ 150, 2"x" + 3"y" ≤ 900​ \$

C) \$ "x" ≥ 100, "y" ≤ 150, 2"x" + 3"y" ≤ 900​ \$

D) \$ "x" ≤ 100, "y" ≥ 150, 2"x" + 3"y" ≥ 900​ \$

Solve the compound inequality and express the solution in interval notation:
\$ −3"x" + 5 > 2 \$ and \$ 4"x" − 7 ≤ 9 \$

A) \$ (−∞, −1) ∪ (−∞, 2)\$

B) \$ (−∞, −2) ∪ (−∞, 4)\$

C) \$ (−∞, −1) ∪ (−∞, 4)\$

D) \$ (−∞, 1) ∪ (−∞, 5)\$

A landscaper is designing a rectangular garden. The length of the garden must be at least 3 meters longer than its width. If the perimeter of the garden is less than or equal to 80 meters, write and solve a system of inequalities to represent the possible dimensions of the garden.

A) ​\$"l" = "w" + 1, "w" ≤ 18.5, "w" ≥ 1 \$​ ​

B) ​\$"l" = "w" + 3, "w" ≤ 12.5, "w" ≥ 0 \$​ ​

C) \$"l" = "w" + 3, "w" ≤ 18.5, "w" ≥ 0 \$​

D) ​\$"l" = "w" + 2, "w" ≤ 18.5, "w" ≥ 0 \$

Find the set of all points (x, y) that satisfy the inequality:
\$ \∣ "x" + "y" − 1\∣ ≤ \∣"x" − "y" + 1\∣ \$

A) \$ \∣ (x, y) \∣ "x" ≤ 1\$ and \$"y" ≤ 1 \$

B) \$ \∣ ("x", "y") \∣ "x" ≤ 1\$ and \$"y" ≤ 0 \$

C) \$ \∣ ("x", "y") \∣ "x" ≤ 0\$ and \$"y" ≤ 1 \$

D) \$ \∣ ("x", "y") \∣ "x" ≤ 0\$ and \$"y" ≤ 0 \$