Water flows back and forth between a small and large tank. When water is moving into a tank the flow rate is positive, and when water is moving from a tank the flow rate is negative. The large tank begins with 300 gallons of water, and
the small tank begins with 200 gallons of water. After a period of 5 minutes, the large tank has the same amount of
water as the small tank. Which statement describes the flow rate?
O The flow rate of the large tank is 10 gal/min, and the flow rate of the small tank is -10 gal/min.
The flow rate of the large tank is -10 gal/min, and the flow rate of the small tank is 10 gal/min.
O The flow rate of the large tank is 20 gal/min, and the flow rate of the small tank is -20 gal/min.
The flow rate of the large tank is -20 gal/min, and the flow rate of the small tank is 20 gal/min.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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step-by-step explanation: