Let us set x for the missing score.
Now, if he wants to keep an average of 86 or greater, we need to use the next inequality:
![(68+84+x)/(3)≥86](https://img.qammunity.org/2023/formulas/mathematics/college/ih6t9hsq26avfl5bateg7adk5bm7hi34ab.png)
Then, we need to solve for x:
![(152+x)/(3)≥86](https://img.qammunity.org/2023/formulas/mathematics/college/vvqh2majlyz3e3hbfmhbckm6n0h1roibky.png)
Multiply both sides by 3:
![\begin{gathered} (3)(152+x)/(3)≥(3)(86) \\ 152+x≥258 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jdqk7fiwypsdadtwi6ufpvh8ojaoqlq11b.png)
Subtract both sides by 152:
![152-152+x≥258-152](https://img.qammunity.org/2023/formulas/mathematics/college/ja0rh9tej1ijadca7uykgf23bolnunalt2.png)
Simplify:
![x≥104](https://img.qammunity.org/2023/formulas/mathematics/college/lddrdo8s4qiurdb4g0hks7o9teabgonjvv.png)
In this case, the score is 104 is greater than the possible number of points.
Hence, enter DNE