Question

A student is solving the inequality -3 + 2y < 4x. The student concludes that the inequality is equivalent to y > 2x + 3. Describe and correct the student's error.

Answer 1

The student's error is that they incorrectly switched the direction of the inequality sign when they solved for y.

Step-by-step explanation:

The student's error is that they incorrectly switched the direction of the inequality sign when they solved for y.

Instead of y > 2x + 3, the correct inequality is y < 2x + 3.

When solving inequalities, it's important to be careful with the direction of the inequality sign. In this case, since -3 + 2y is less than 4x, we want the values of y that make the expression on the left smaller than the expression on the right, so y should be less than 2x + 3.