To solve the inequality
\[ \frac{t}{4} \geq -3, \]
we will follow these steps:
Step 1: Eliminate the fraction
To eliminate the fraction, we multiply both sides of the inequality by 4. Since 4 is a positive number, the direction of the inequality does not change.
\[ 4 \cdot \frac{t}{4} \geq 4 \cdot (-3) \]
This simplifies to:
\[ t \geq -12. \]
Solution
The solution to the inequality is
\[ t \geq -12. \]
Part 2: Properties of Inequalities Used
In this step, we can identify which properties of inequalities we used to obtain the solution.
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A. Multiplication property of inequality: This property states that if you multiply both sides of an inequality by a positive number, the direction of the inequality stays the same. We used this property when we multiplied both sides by 4.
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B. Addition property of inequality: This property states that if you add the same number to both sides of an inequality, the direction of the inequality stays the same. We did not use this property for our solution.
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C. Subtraction property of inequality: This property states that if you subtract the same number from both sides of an inequality, the direction of the inequality stays the same. We did not use this property for our solution.
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D. Division property of inequality: This property states that if you divide both sides of an inequality by a positive number, the direction of the inequality stays the same. We did not use this property, as we multiply by 4 instead.
Selected Properties
The only relevant property used in solving the inequality is:
A. Multiplication property of inequality.
Remember to provide your final answer in the context you need. Here, the solution is \( t \geq -12 \) and the property used is the multiplication property of inequality.