Question

Kennedy graphed the inequality x^2 - 4x + 3 < 0 and concluded that the solution is x < 1 or x > 3. What mistake did she make, and what is the correct solution?

A) The mistake was not graphing it correctly, and the correct solution is x > 1 and x < 3.
B) The mistake was using the wrong inequality sign, and the correct solution is x > 1 and x < 3.
C) The mistake was not graphing it correctly, and the correct solution is x < 1 or x > 3.
D) The mistake was using the wrong inequality sign, and the correct solution is x < 1 or x > 3.

Answer 1

Kennedy's mistake was in interpreting the graph's solution. The inequality x^2 - 4x + 3 < 0 is true for x values between 1 and 3, leading to the correct answer of x > 1 and x < 3.

Step-by-step explanation:

Kennedy made a mistake in interpreting the solutions to the inequality x^2 - 4x + 3 < 0. Factoring the quadratic equation gives us (x - 1)(x - 3) < 0. To find the solution set, we look for values of x that make the expression negative. By testing intervals, we see that the inequality is true for values of x between 1 and 3. Thus, the correct solution is x > 1 and x < 3, which means that the correct answer is Option A: The mistake was not graphing it correctly, and the correct solution is x > 1 and x < 3.