If `x gt 5` and `y lt -1`, then which of the following statements is true ?

Options

A. `(x + 4y) gt 1`
B. `x gt -4y`
C. `-4x lt 5y`
D. None of these

Answer

To solve the problem, we need to analyze the given inequalities and evaluate the options based on the conditions provided: \( x > 5 \) and \( y < -1 \).

**Step 1: Choose values for \( x \) and \( y \)**
Given \( x > 5 \), we can choose \( x = 6 \).
Given \( y < -1 \), we can choose \( y = -2 \).
So, we have \( x = 6 \) and \( y = -2 \).

**Step 2: Evaluate Option A**
Option A states: \( x + 4y \).
Substituting the values:
\[ x + 4y = 6 + 4(-2) = 6 - 8 = -2 \]
Now, we check if \(-2 > 1\). This is false.

**Step 3: Evaluate Option B**
Option B states: \( x > -4y \).
Substituting the values:
\[ x > -4y \implies 6 > -4(-2) \implies 6 > 8 \]
This is false.

**Step 4: Evaluate Option C**
Option C states: \( -4x < 5y \).
Substituting the values:
\[ -4x < 5y \implies -4(6) < 5(-2) \implies -24 < -10 \]
This is false.

**Step 5: Evaluate Option D**
Since all previous options (A, B, and C) are false, we conclude that Option D, which states "none of these," must be true.

Thus, the answer is: **None of these.**

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