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solve the inequality and graph the solution. \\(\\frac{v}{2} + 9 > 6\\)…

Question

solve the inequality and graph the solution.
\\(\frac{v}{2} + 9 > 6\\)
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.
\\(\leftarrow\\) \\(\vert\\) \\(-10\\) \\(\vert\\) \\(-8\\) \\(\vert\\) \\(-6\\) \\(\vert\\) \\(-4\\) \\(\vert\\) \\(-2\\) \\(\vert\\) \\(0\\) \\(\vert\\) \\(2\\) \\(\vert\\) \\(4\\) \\(\vert\\) \\(6\\) \\(\vert\\) \\(8\\) \\(\vert\\) \\(10\\) \\(\
ightarrow\\)

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \( v \), we subtract 9 from both sides of the inequality \(\frac{v}{2}+9 > 6\). This gives us \(\frac{v}{2}+9 - 9>6 - 9\), which simplifies to \(\frac{v}{2}>- 3\).

Step2: Multiply both sides by 2

To solve for \( v \), we multiply both sides of the inequality \(\frac{v}{2}>-3\) by 2. This gives us \(\frac{v}{2}\times2>-3\times2\), which simplifies to \(v > - 6\).

Answer:

The solution to the inequality is \(v > - 6\). To graph this, we plot an open circle at \(-6\) (since the inequality is strict, \(v
eq - 6\)) and draw a ray to the right of \(-6\) on the number line.