Question

solve the inequality and graph the solution.
\frac{5}{2} > 2
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.
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work it out
not feeling ready yet? these can help:
graph inequalities
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lesson: solving inequalities
lesson: inequalities on a number line

Explanation:

Step 1: Solve the inequality

We have the inequality \(\frac{x}{2}>2\). To solve for \(x\), we multiply both sides of the inequality by \(2\) (since \(2\) is positive, the direction of the inequality sign remains the same).

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Step 2: Graph the solution

To graph \(x > 4\) on the number line:

• We use an open circle at \(4\) because \(x\) is not equal to \(4\) (the inequality is strict, \(>\) not \(\geq\)).
• Then we draw an arrow to the right of \(4\) to represent all the numbers greater than \(4\).

Answer:

The solution to the inequality \(\frac{x}{2}>2\) is \(x > 4\). For the graph, place an open circle at \(4\) and draw an arrow pointing to the right.