If the point (a, 2a) lies between the lines | | vedclass

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(A) The equation $|x + y + 1| = 4$ represents two parallel lines:$x + y + 1 = 4 \implies x + y - 3 = 0$$x + y + 1 = -4 \implies x + y + 5 = 0$For the

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$(-5/3, 1)$

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(A) The equation $|x + y + 1| = 4$ represents two parallel lines:$x + y + 1 = 4 \implies x + y - 3 = 0$$x + y + 1 = -4 \implies x + y + 5 = 0$For the point $(a, 2a)$ to lie between these two lines,the expressions $(x + y - 3)$ and $(x + y + 5)$ must have opposite signs at the point $(a, 2a)$.Substituting $(a, 2a)$ into the expressions:$(a + 2a - 3)(a + 2a + 5) $(3a - 3)(3a + 5) $9(a - 1)(a + 5/3) $(a - 1)(a + 5/3) This inequality holds when $a$ is between the roots:$a \in (-5/3, 1)$

If the point $(a, 2a)$ lies between the lines $|x + y + 1| = 4$,then the complete set of values of $'a'$ is:

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