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Which of the following points is a solution of the inequality [tex]y \ \textless \ -|x|[/tex]?

A. [tex]\((1,0)\)[/tex]
B. [tex]\((1,-1)\)[/tex]
C. [tex]\((1,-2)\)[/tex]



Answer :

GinnyAnswer
To determine which of the points is a solution to the inequality [tex]\( y < -|x| \)[/tex], we need to check each point against this inequality step-by-step.

### Check Point (1, 0)
1. For [tex]\( (1, 0) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = 0 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( 0 < -1 \)[/tex]
- This is false.

### Check Point (1, -1)
2. For [tex]\( (1, -1) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -1 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -1 < -1 \)[/tex]
- This is false.

### Check Point (1, -2)
3. For [tex]\( (1, -2) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -2 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -2 < -1 \)[/tex]
- This is true.

After evaluating all the points, we see that the point [tex]\((1, -2)\)[/tex] satisfies the inequality [tex]\( y < -|x| \)[/tex].

Therefore, the point which is a solution of the inequality [tex]\( y < -|x| \)[/tex] is [tex]\((1, -2)\)[/tex].

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