Respuesta :
Answer: The correct option is (B) [tex]y-7<2x-6.[/tex]
Step-by-step explanation: We are given to select the inequalities that has the point (0, 0) as a solution.
Option (A):
The given inequality is
[tex]y+7<2x+6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x+6=2\times0+6=6.[/tex]
Since 7 > 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (B):
The given inequality is
[tex]y-7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-7=0-7=-7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since -7 < - 6, so the point (0, 0) is a solution to this inequality.
This option is correct.
Option (C):
The given inequality is
[tex]y-6<2x-7.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-6=0-6=-6,\\\\R.H.S.=2x-7=2\times0-7=-7.[/tex]
Since -6 > - 7, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (D):
The given inequality is
[tex]y+7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since 7 > - 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Thus, the point (0, 0) is a solution to the inequality [tex]y-7<2x-6.[/tex]
Option (B) is correct.
