Solve the inequality and graph the solution.

Question

5(r+3)+9<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.

Answer 1

To solve the inequality \( 5(r + 3) + 9 < 4 \), we will start by simplifying the expression.

1. Distribute the \( 5 \): \[ 5r + 15 + 9 < 4 \]

2. Combine like terms: \[ 5r + 24 < 4 \]

3. Subtract \( 24 \) from both sides: \[ 5r < 4 - 24 \] \[ 5r < -20 \]

4. Divide both sides by \( 5 \): \[ r < -4 \]

Graphing the solution

The solution \( r < -4 \) means that \( r \) can take any value less than \(-4\).

• Endpoint: The endpoint is \(-4\).
• Closed/Open: Since the inequality is strict (\(<\)), we will use an open circle at \(-4\) to indicate that \(-4\) is not included in the solution.

Graph

On a number line, we will:

1. Place an open circle at \(-4\).
2. Shade to the left of \(-4\) to indicate all numbers less than \(-4\).

Number Line Representation:

<---o========================>
    -5  -4  -3  -2  -1  0

• The open circle at \(-4\) indicates that \(-4\) is not part of the solution, and the shaded area to the left represents all values less than \(-4\).