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Part 1
Solve the following inequality. Justify each step.
negative 4 less than or equals StartFraction t Over 7 EndFraction
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Part 1
What is the​ solution?
  
t greater than or equals minus 28
​(Simplify your answer. Type an​ inequality.)
Part 2
Select all properties of inequalities used to obtain the solution.
A.
Subtraction property of inequality
B.
Addition property of inequality
C.
Multiplication property of inequality
D.
Division property of inequality

1 answer

To solve the inequality \(-4 \leq \frac{t}{7}\), follow these steps:

  1. Multiply both sides by 7: Since we're multiplying by a positive number, the direction of the inequality does not change. \[ -4 \cdot 7 \leq \frac{t}{7} \cdot 7 \] This simplifies to: \[ -28 \leq t \] or equivalently, \[ t \geq -28 \]

Solution: The solution is \(t \geq -28\).

Part 2: Properties of Inequalities Used

In this case, the relevant property is:

  • D. Division property of inequality (since you essentially multiplied both sides by 7, which is indeed a form of scaling the inequality).

However, since we used multiplication (and multiplication is essentially a quicker way to think of division in context here), we can say:

  • C. Multiplication property of inequality is also correct.

So for clarity, you would select:

  • C. Multiplication property of inequality.

The other options (A. Subtraction and B. Addition) are not used in this solution.