Answered

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Question 6 (Multiple Choice, Worth 4 points)

Which of the following is a solution to this inequality?

[tex]\[ y \ \textless \ \frac{2}{3} x + 2 \][/tex]

A. (0, 0)

B. (3, 3)

C. (3, 4)

D. (1, 1)

Sagot :

GinnyAnswer
To determine which of the following options is a solution to the inequality [tex]\( y < \frac{2}{3} x + 2 \)[/tex], we can check different points and see if they satisfy the inequality.

Let's analyze the point (0, 0):

1. Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality:
[tex]\[ y < \frac{2}{3} x + 2 \][/tex]

2. This becomes:
[tex]\[ 0 < \frac{2}{3} \cdot 0 + 2 \][/tex]
[tex]\[ 0 < 0 + 2 \][/tex]
[tex]\[ 0 < 2 \][/tex]

The inequality [tex]\( 0 < 2 \)[/tex] is true, which means the point (0, 0) satisfies the inequality:

Therefore, the point [tex]\( (0,0) \)[/tex] is a solution to the inequality [tex]\( y < \frac{2}{3} x + 2 \)[/tex].
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