To solve the inequality \( \frac{g}{2} + 14 \geq 15 \), we will isolate \( g \) step by step.
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Start by subtracting 14 from both sides:
\[ \frac{g}{2} + 14 - 14 \geq 15 - 14 \]
This simplifies to:
\[ \frac{g}{2} \geq 1 \]
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Next, multiply both sides by 2 to eliminate the fraction (note that since we are multiplying by a positive number, the inequality direction remains the same):
\[ g \geq 2 \]
So the solution to the inequality is:
\[ g \geq 2 \]
Graphing the Solution
To graph this solution on a number line:
- Draw a number line.
- Place a closed circle at \( g = 2 \) to indicate that \( 2 \) is included in the solution (because of the "greater than or equal to" part).
- Shade to the right of \( 2 \) to indicate all values greater than \( 2 \) are included in the solution.
The graph looks like this:
---|----|----|----|----|----|----|----|----|----|----|----|----|--->
-2 -1 0 1 2 3 4 5 6 7 8 9 10
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In this representation:
- The closed circle at \( 2 \) indicates that \( 2 \) is included in the solution set.
- The arrow to the right signifies all values greater than \( 2 \) are included.