Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/acd7fc66-8fa8-4701-80b9-5b36b296f970/result_image/1599211909.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001238Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1adcfabbc1f29332c55713c23f822e4f11ae0de56e8fb863a71ec6eb10c682c7)
Work Step by Step
Given: $\frac{1}{2}x+3y \gt 8$
The solution region is above and not including the dashed boundary line.
Take one point in the region and test $(4,3)$:
$\frac{1}{2}.4+3.3 \gt 8$
$11 \gt8\rightarrow$ True
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