To solve the inequality \( 6 > \frac{p}{12} \), we can follow these steps:
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Multiply both sides of the inequality by 12 to eliminate the fraction. Remember that since 12 is a positive number, the direction of the inequality does not change.
\[ 6 \cdot 12 > p \]
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Calculate \( 6 \cdot 12 \):
\[ 72 > p \]
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To express this inequality more conventionally, we can rewrite it:
\[ p < 72 \]
Thus, the solution to the inequality is:
\[ p < 72 \]
Part 2: Graphing the solution
To graph the solution \( p < 72 \):
- Draw a number line.
- Place an open circle at 72 (indicating that 72 is not included in the solution).
- Shade the area to the left of 72 to represent all numbers less than 72.
Check the Solution
To check if the solution is correct, we can substitute a number that satisfies the inequality (i.e., any number less than 72).
For example, if we try \( p = 70 \):
\[ 6 > \frac{70}{12} \]
Calculating the right side:
\[ \frac{70}{12} \approx 5.833 \]
And we see:
\[ 6 > 5.833 \quad \text{(True)} \]
Now check a number that does NOT satisfy the inequality, for example, \( p = 75 \):
\[ 6 > \frac{75}{12} \]
Calculating the right side:
\[ \frac{75}{12} \approx 6.25 \]
And we see:
\[ 6 > 6.25 \quad \text{(False)} \]
This confirms that our solution \( p < 72 \) is correct.