Exercise 3 Page 899

We want to know which point is not a solution of the given inequality. We can determine whether each point $(x,y)$ is a solution by substituting its values into the inequality and simplifying it. If it leads to a false statement, then it is not a solution of the inequality. Let's start with the point $A(0,0),$ we can determine if it is a solution by substituting $0$ for $x$ and $0$ for $y.$ Since $0>\text{-}1$ is a true statement, $(0,0)$ is a solution of the inequality. Now, let's repeat the same for the next options.

Option	Point	Substitute	Simplify	Solution?
A	$(0,0)$	$0>2|0+3|-7$	$0>\text{-}1$	$✓$
B	$(1,1)$	$\text{-}1>2|\text{-}2+3|-7$	$\text{-}1>\text{-}5$	$✓$
C	$(\text{-}2,\text{-}1)$	$1>2|1+3|-7$	$1>1$	$\times$
D	$(\text{-}1,1)$	$1>2|\text{-}1+3|-7$	$1>\text{-}3$	$✓$

As we can see, the substitution of $(\text{-}2,\text{-}1)$ led to $1>1,$ which is a false statement, while the other points led to true statements. Because of that, only $(1,1)$ is not a solution of the inequality. Since we are looking for the point that is not a solution of the inequality, C is the correct option.