Question

Which of the following is a solution to this inequality? y less than two thirds times x plus 2 (0, 3) (−3, 1) (3, 5) (1, 2)

Answer 1

In evaluating the provided pairs for the inequality y < (2/3)x + 2, the pairs (-3, 1) and (1, 2) satisfy the inequality and are therefore solutions.

Step-by-step explanation:

The student has asked for a solution to an inequality of the form y < (2/3)x + 2. To determine which of the given pairs is a solution, we can substitute the x and y values into the inequality and check for truthfulness. For example, using the pair (0,3), we get 3 < (2/3)(0) + 2, which simplifies to 3 < 2, an incorrect statement, so (0,3) is not a solution. Following this method, let's check the other pairs:

• For (-3, 1): 1 < (2/3)(-3) + 2 equals 1 < -2 + 2 equals 1 < 0, which is true, so (-3, 1) is a solution.
• For (3, 5): 5 < (2/3)(3) + 2 equals 5 < 2 + 2 equals 5 < 4, which is false, so (3, 5) is not a solution.
• For (1, 2): 2 < (2/3)(1) + 2 equals 2 < 2/3 + 2 equals 2 < 2.66, which is true, so (1, 2) is a solution.

Therefore, the solutions to the inequality from the given pairs are (-3, 1) and (1, 2).

Answer 2

D, (1,2)

Step-by-step explanation:

If we graph this, and shade under since it is "<", all we have to do is find a point that is in the shaded area. The only one in the shaded area is, (1,2).