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If x, y and b are real number and x lt ...

If x, y and b are real number and ` x lt y, b lt 0`, then

A

`x/b lt y/b`

B

`x/b le y/b`

C

`x/b gt y/b`

D

`x/b ge y/b`

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The correct Answer is:
To solve the problem step by step, we start with the given inequalities and the properties of inequalities involving negative numbers. ### Step 1: Understand the Given Inequalities We are given: 1. \( x < y \) 2. \( b < 0 \) ### Step 2: Divide by the Negative Number Since \( b \) is negative, we need to remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign. ### Step 3: Apply the Division Now, we divide both sides of the inequality \( x < y \) by \( b \): \[ \frac{x}{b} \quad \text{and} \quad \frac{y}{b} \] ### Step 4: Reverse the Inequality Since \( b < 0 \), we reverse the inequality: \[ \frac{x}{b} > \frac{y}{b} \] ### Conclusion Thus, the final result is: \[ \frac{x}{b} > \frac{y}{b} \] ### Correct Option The correct option from the choices given is: \[ \frac{x}{b} > \frac{y}{b} \] ---
To solve the problem step by step, we start with the given inequalities and the properties of inequalities involving negative numbers. ### Step 1: Understand the Given Inequalities We are given: 1. \( x < y \) 2. \( b < 0 \) ### Step 2: Divide by the Negative Number ...
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