Problem in inequalities...... Help!!!!

solve: |4-x|+1<1

Note by Akash Sinha
4 years, 9 months ago

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\(|4-x| + 1 < 1\)

Simplifying, we get-

\(|4-x| < 0\)

But since the LHS is in Modulus, it has to be positive or equal to zero. Hence, the above inequality holds for no real numbers.

Akshat Jain - 4 years, 9 months ago

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From the given inequality ,

\(| 4-x | < 0\)

But since we know , for any \(a \in \mathbb{R} \)

\[ | a | = \begin{cases} -a & \text{if } x < 0 \\ a & \text{if } x \geq 0 \end{cases} \]

also , \( | a | \geq 0 \)

But here , \(| 4-x | < 0\) , which is not possible .

Thus no such Real values are there for x .

Priyansh Sangule - 4 years, 9 months ago

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