Solve the following inequality. Justify each step.

Question

StartFraction t Over 4 EndFraction greater than or equals minus 3
Question content area bottom
Part 1
What is the​ solution?
  
t greater than or equals minus 12
​(Simplify your answer. Type an​ inequality.)
Part 2
Select all properties of inequalities used to obtain the solution.
A.
Division property of inequality
B.
Addition property of inequality
C.
Subtraction property of inequality
D.
Multiplication property of inequality

Answer 1

To solve the inequality:

\[ \frac{t}{4} \geq -3 \]

we follow these steps:

Part 1: Solve the Inequality

1. Multiply both sides by 4: Since 4 is positive, the direction of the inequality does not change.

   \[ 4 \cdot \frac{t}{4} \geq 4 \cdot (-3) \]

2. Simplify:

   \[ t \geq -12 \]

So the solution is:

\[ t \geq -12 \]

Part 2: Properties of Inequalities Used

In this step, we multiplied both sides of the inequality by a positive number (4). Therefore, the properties used in the solution are:

• A. Division property of inequality (was not used here, we multiplied)
• B. Addition property of inequality (was not used here)
• C. Subtraction property of inequality (was not used here)
• D. Multiplication property of inequality (was used here)

Final Answer:

• Solution: \( t \geq -12 \)
• Selected Property: D. Multiplication property of inequality