A student attempts to solve the following compound inequality 2−3x>8 OR 5x−2>13. If the solution is incorrect, where did the student first go wrong and why?
1. Solve 2−3x>8. x<−2
2. Solve 5x−2>13. x>3
3. Recombine the solutions. −2<x<3(1 point)
Responses
The solution to the first branch is incorrect because the direction of the inequality was switched when it should not have been.
The solution to the first branch is incorrect because the direction of the inequality was switched when it should not have been.
No mistake has been made.
No mistake has been made.
In step 3, the recombination of the two branches of the compound inequality is incorrect. They are merged as if they are an AND inequality, when they should be merged as an OR inequality.
In step 3, the recombination of the two branches of the compound inequality is incorrect. They are merged as if they are an AND inequality, when they should be merged as an OR inequality.
In step 2, the solution is incorrect. It should be x<3 because when you add a negative number, you have to switch the direction of the inequality.
The correct response is: The solution to the first branch is incorrect because the direction of the inequality was switched when it should not have been.
In step 1, the student correctly solved the inequality 2−3x>8 and determined that x<-2. However, they made the mistake of switching the direction of the inequality to x>-2. This is incorrect because when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality should be reversed. The correct solution should be x<-2.