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(C) The equation $|x + y| = 2$ represents two parallel lines: $x + y = 2$ and $x + y = -2$.The point $(a, a)$ lies on the line $y = x$.To find the ran

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$|a| < 1$

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(C) The equation $|x + y| = 2$ represents two parallel lines: $x + y = 2$ and $x + y = -2$.The point $(a, a)$ lies on the line $y = x$.To find the range of $a$ such that the point $(a, a)$ lies between these two lines,we substitute $x = a$ and $y = a$ into the equations of the lines:For $x + y = 2$,we get $a + a = 2$,which implies $2a = 2$,so $a = 1$.For $x + y = -2$,we get $a + a = -2$,which implies $2a = -2$,so $a = -1$.Since the point $(a, a)$ must lie between the lines $x + y = 2$ and $x + y = -2$,the value of $a$ must satisfy $-1 This inequality is equivalent to $|a| < 1$.

If the point $(a, a)$ lies between the lines $|x + y| = 2$,then

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