Chapter 6, Problem 17CT

To determine

To find: the correct student error with the help of given information.

Answer to Problem 17CT

The student makes a mistake by taking solution $\left(-2,-1\right)$ instead of $\left(-1,-2\right)$

So, the correct solution is $\left(-1,-2\right)$

Explanation of Solution

Given information:

A student concluded $\left(-2,-1\right)$ is a solution of the inequality $y<3x+2$

Calculation:

Consider the inequality

  $y<3x+2$

Check at $\left(-2,-1\right)$

  $y<3x+2$

  $-1<3(-2)+2$

  $-1<-6+2$

  $-1<-4$

Hence, the solution $\left(-2,-1\right)$ is not appropriate Now, check the inequality at $\left(-1,-2\right)$

  $y<3x+2$

  $-2<3(-1)+2$

  $-2<-3+2$

  $-2<-1$

Student makes a mistake by taking solution $\left(-2,-1\right)$ instead of $\left(-1,-2\right)$

Therefore, the correct solution is $\left(-1,-2\right)$