Which inequality is equivalent to [tex]7x - 2y > 8[/tex]?
A) [tex]y > \frac{7}{2}x + 8[/tex]
B) [tex]y > -\frac{2}{7}x + \frac{8}{7}[/tex]
C) [tex]y < \frac{7}{2}x - 4[/tex]
D) [tex]y < -\frac{2}{7}x - \frac{4}{7}[/tex]
Answer (3)
8 \ \ -7x \\ \\7x -7x-2y> 8 -7x \\ \\ -2y >8-7x \ \ / : (-2)\\ \\\frac{-2}{-2}\cdot y < \frac{8}{(-2)}-\frac{7}{(-2)}x \\ \\ y < \frac{7}{ 2}x -4 \\ \\ \\ Answer : \ c) \ y < \frac{7}{2}x-4"> 7 x − 2 y > 8 − 7 x 7 x − 7 x − 2 y > 8 − 7 x − 2 y > 8 − 7 x / : ( − 2 ) − 2 − 2 ⋅ y < ( − 2 ) 8 − ( − 2 ) 7 x y < 2 7 x − 4 A n s w er : c ) y < 2 7 x − 4
I f w e m u lt i pl y or d i v i d e b o t h s i d es o f an in e q u a l i t y b y a n e g a t i v e n u mb er w e ha v e t o s w i t c h t h e d i rec t i o n o f t h e in e q u a l i t y
The student is asking which inequality is equivalent to 7x - 2y > 8. An inequality shows how one expression compares to another by indicating that one is greater than, less than, or equal to the other. To find the equivalent inequality in terms of y, we can solve the given inequality for y:
Subtract 7x from both sides of the inequality: -2y > -7x + 8.
Divide both sides by -2, and remember to reverse the inequality sign because we are dividing by a negative number: y < (7/2)x - 4.
The equivalent inequality in terms of y is option (c) y < 7/2x - 4.
The equivalent inequality to 8"> 7 x − 2 y > 8 is y < 2 7 x − 4 . Thus, the correct answer is option C. It's important to remember that when dividing by a negative number in inequalities, the direction of the inequality sign changes.
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