IXL Spotlight - Geometry > F.11 Graph solutions to advanced linear inequalities 5GC
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Questions
answered
Solve the inequality and graph the solution.
\[
3(u+6)+10> 4
\]
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.
Submit
Answer
\(\boxed{\text{The solution to the inequality } 3(u+6)+10>4 \text{ is } u > -8. \text{ This is represented on the number line as an open circle at -8, with a green line extending to the right of -8, indicating all values greater than -8.}}\)
Step 1 ：The question is asking to solve the inequality \(3(u+6)+10>4\) and graph the solution.
Step 2 ：First, we need to simplify the inequality. We can do this by distributing the 3 to both u and 6, then subtracting 10 from both sides.
Step 3 ：After simplifying, we can solve for u by dividing both sides by 3.
Step 4 ：The solution to the inequality is \(u > -8\). This means that all values of u that are greater than -8 are solutions to the inequality.
Step 5 ：Now, we need to graph this solution on a number line. Since the inequality is 'greater than' and not 'greater than or equal to', we will use an open circle to represent the endpoint at -8.
Step 6 ：\(\boxed{\text{The solution to the inequality } 3(u+6)+10>4 \text{ is } u > -8. \text{ This is represented on the number line as an open circle at -8, with a green line extending to the right of -8, indicating all values greater than -8.}}\)
