To solve the inequality \(3(q + 27) > 63\), follow these steps:
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Start by distributing the \(3\): \[ 3q + 81 > 63 \]
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Next, subtract \(81\) from both sides: \[ 3q > 63 - 81 \] \[ 3q > -18 \]
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Finally, divide both sides by \(3\): \[ q > -6 \]
The solution to the inequality is \(q > -6\).
Endpoint Selection
- The endpoint here is \(-6\).
- Since \(q > -6\) does not include \(-6\), we will represent it as an open endpoint.
Graphing the Solution
- Plot the point \(-6\) on the number line with an open circle (since \(-6\) is not included).
- Shade the area to the right of \(-6\) to represent all values greater than \(-6\).
Here's a rough sketch of what the number line looks like:
<---|----|----|----|----|----|----|----|----|----|--->
-8 -7 -6 -5 -4 -3 -2 -1 0
( )
In this graph:
- The open circle at \(-6\) indicates that \(-6\) is not part of the solution.
- The shading to the right illustrates that all values greater than \(-6\) are included in the solution.