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Solve the inequality and graph the solution.

3(q+27)>63
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.

1 answer

To solve the inequality \(3(q + 27) > 63\), follow these steps:

  1. Start by distributing the \(3\): \[ 3q + 81 > 63 \]

  2. Next, subtract \(81\) from both sides: \[ 3q > 63 - 81 \] \[ 3q > -18 \]

  3. 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

  1. Plot the point \(-6\) on the number line with an open circle (since \(-6\) is not included).
  2. 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.