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If d > a and L < a, which of the followi...

If `d > a and L < a`, which of the following cannot be true?

A

`d + L = 14`

B

`d - L = 7`

C

`d - L = 1`

D

`a - d = 9`

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the given inequalities and determine which of the options cannot be true based on the conditions \(d > a\) and \(L < a\). ### Step-by-step Solution: 1. **Understand the Given Conditions:** - We have two inequalities: - \(d > a\) (which implies \(d - a > 0\)) - \(L < a\) (which implies \(L - a < 0\)) 2. **Rearranging the Inequalities:** - From \(d > a\), we can rearrange it to \(a - d < 0\). - From \(L < a\), we can rearrange it to \(a - L > 0\). 3. **Analyzing Each Option:** - We need to evaluate each option provided in the question to see if they can be true or not. 4. **Option Analysis:** - **Option 1:** \(D + L = 14\) - We cannot determine if this is true or false based on the inequalities alone, so it might be true. - **Option 2:** \(D - L = 1\) - Since \(d > a\) and \(L < a\), it implies \(d > L\). Therefore, \(D - L > 0\) which can be true. - **Option 3:** \(D - L = 7\) - Similar to option 2, since \(d > L\), \(D - L > 0\) which can also be true. - **Option 4:** \(A - D = 9\) - Rearranging gives \(A = D + 9\). Since \(d > a\), this means \(d\) cannot be \(A + 9\) (as \(d\) would have to be less than \(A\)), which contradicts \(d > a\). Thus, this option cannot be true. 5. **Conclusion:** - The option that cannot be true is **Option 4: \(A - D = 9\)**.
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