# 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.

- 4 years, 9 months ago

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 .

- 4 years, 9 months ago