Absolute Value Question 1

If $ | 2x+5 |=7 $ and $| 3y+6 | = 12$, which of the following is not a possible value of $ |xy| $ ?

$-12$

$6$

$2$

$36$

Approach

Solving for $x \text{ and } y$:

$2x+5=7$

$$ 2x=2 $$ $$ x=1 $$

$2x+5=-7$

$$ 2x=-12 $$ $$ x=-6 $$

$3y+6=12 $

$$ 3y=6 $$ $$ y=2 $$

$3y+6=-12$

$$ 3y=-18 $$ $$ y=-6 $$

$$ x=1 \text{ or } -6 $$ $$ y=2 \text{ or } -6 $$

Possible values of $xy$ are:

$$ 1 \cdot 2 =2$$ $$ 1 \cdot -6 = -6 $$ $$ -6 \cdot 2 = -12 $$ $$ -6 \cdot -6 = 36 $$