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The point [tex]$(0,0)$[/tex] is a solution to which of these inequalities?

A. [tex]y + 7 \ \textless \ 2x - 6[/tex]
B. [tex]y - 6 \ \textless \ 2x - 7[/tex]
C. [tex]y - 7 \ \textless \ 2x - 6[/tex]
D. [tex]y + 7 \ \textless \ 2x + 6[/tex]

Sagot :

GinnyAnsweridn
To determine which of the inequalities the point [tex]\((0,0)\)[/tex] satisfies, we need to substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex] into each inequality and check if the resulting statement is true.

Let's analyze each inequality one by one:

### Inequality A: [tex]\( y + 7 < 2x - 6 \)[/tex]

Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex]:
[tex]\[ 0 + 7 < 2(0) - 6 \][/tex]
[tex]\[ 7 < -6 \][/tex]
This statement is false.

### Inequality B: [tex]\( y - 6 < 2x - 7 \)[/tex]

Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex]:
[tex]\[ 0 - 6 < 2(0) - 7 \][/tex]
[tex]\[ -6 < -7 \][/tex]
This statement is false.

### Inequality C: [tex]\( y - 7 < 2x - 6 \)[/tex]

Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex]:
[tex]\[ 0 - 7 < 2(0) - 6 \][/tex]
[tex]\[ -7 < -6 \][/tex]
This statement is true.

### Inequality D: [tex]\( y + 7 < 2x + 6 \)[/tex]

Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex]:
[tex]\[ 0 + 7 < 2(0) + 6 \][/tex]
[tex]\[ 7 < 6 \][/tex]
This statement is false.

So, after evaluating the inequalities with the point [tex]\((0,0)\)[/tex], we find that the point [tex]\((0,0)\)[/tex] is a solution only to inequality [tex]\( \text{C}. \)[/tex]
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