Chapter 2.1, Problem 28E

To determine

To identify:

Correct the error and given solution $8$ is in solution set of the inequality or not.

Answer to Problem 28E

Given solution $x=8$ is a solution of the inequality as $6\le 6$ is a true statement then $8$ should be in the solution set.

Explanation of Solution

Given information:

  $\frac{1}{2}x+2\le 6$

Solution $=8$

Calculation:

For converting the given equation as an inequality,

Consider the variables and numbers that go on the left hand side and right hand side.

Given equation is,

  $\frac{1}{2}x+2\le 6$

Given solution is $8$ ,

Now, put $8$ in above equation,

  $\begin{array}{l}\frac{1}{2}\left(8\right)+2\le 6\\ 4+2\le +6\\ 6\le 6\end{array}$

Hence, error made a wrong conclusion, as $6\le 6$ is a true statement, then $8$ should be in the solution set.

The error is it made a wrong conclusion, as $6\le 6$ is a true statement.