To solve the inequality \( 92 \geq 46(s - 6) \), we first simplify the expression on the right side:
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Distribute \( 46 \): \[ 92 \geq 46s - 276 \]
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Next, add \( 276 \) to both sides of the inequality: \[ 92 + 276 \geq 46s \] \[ 368 \geq 46s \]
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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:
- On a number line, plot the point \( 8 \).
- Since the solution includes \( 8 \) (indicated by “less than or equal to”), we use a closed dot on \( 8 \).
- 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:
- We will keep the closed dot at \( 8 \).
- To change an endpoint from closed to open, let’s change the direction of our shading to use an open circle at \( 8 \).
- 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.