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Solve the following : (i) |x-2|=(x-2) ...

Solve the following :
(i) `|x-2|=(x-2) " (ii) " |x+3| = -x-3`
(iii) `|x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)`

Text Solution

AI Generated Solution

Let's solve each part of the question step by step. ### Part (i): Solve `|x - 2| = x - 2` 1. **Understanding the Modulus**: The equation `|x - 2| = x - 2` implies that the expression inside the modulus must be non-negative. Therefore, we can write: \[ x - 2 \geq 0 \quad \Rightarrow \quad x \geq 2 \] ...
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