Solve the inequality and graph the solution.

Question

92≥46(s–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.

Answer 1

To solve the inequality \( 92 \geq 46(s - 6) \), we first simplify the expression on the right side:

1. Distribute \( 46 \): \[ 92 \geq 46s - 276 \]

2. Next, add \( 276 \) to both sides of the inequality: \[ 92 + 276 \geq 46s \] \[ 368 \geq 46s \]

3. Now, divide both sides by \( 46 \): \[ \frac{368}{46} \geq s \] \[ 8 \geq s \]

This can also be written as: \[ s \leq 8 \]

The solution to the inequality is \( s \leq 8 \).

Graphing the Solution:

To graph this solution:

1. On a number line, plot the point \( 8 \).
2. Since the solution includes \( 8 \) (indicated by “less than or equal to”), we use a closed dot on \( 8 \).
3. Shade to the left of \( 8 \) to indicate all the values of \( s \) that are less than or equal to \( 8 \).

To modify the graph as requested:

1. We will keep the closed dot at \( 8 \).
2. To change an endpoint from closed to open, let’s change the direction of our shading to use an open circle at \( 8 \).
3. We can delete the shading to the right of \( 8 \) since it isn't part of the solution.

Final Graph:

• Place an open circle at \( 8 \).
• Shade everything to the left of \( 8 \) indicating all numbers less than \( 8 \).

This represents the solution accurately, showing that \( s \) can take any value less than \( 8 \) but not including \( 8 \) itself.