allimiley2010
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Which inequality is equivalent to this thing that I don’t know how to explain but plssss help it would mean a lot and I can’t get any others wrong or I’ll fail the lesson help plss

Which inequality is equivalent to this thing that I dont know how to explain but plssss help it would mean a lot and I cant get any others wrong or Ill fail the class=

Respuesta :

-6x ≥ 30   Divide -6 on both sides to get "x" by itself

[tex]\frac{-6x}{-6}\geq \frac{30}{-6}[/tex]  When you divide/multiply a negative number in an inequality, you flip the sign >/<

x ≤ -5   Your answer is the bottom right option

Answer:  [tex]x \le -5[/tex] (lower right hand corner)

To get this answer, you would divide both sides by -6 to undo the multiplication. When you multiply or divide both sides of an inequality by a negative number, the inequality sign will flip.

So,

[tex]-6x \ge 30[/tex]

[tex]-6x/(-6) \le 30/(-6)[/tex] ... dividing both sides by -6; inequality sign flips

[tex]x \le -5[/tex]

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The longer way to do the problem would be to do it like this

[tex]-6x \ge 30[/tex]

[tex]-6x+6x \ge 30+6x[/tex] .... adding 6x to both sides

[tex]0 \ge 30+6x[/tex]

[tex]30+6x \le 0[/tex]

[tex]6x+30 \le 0[/tex]

[tex]6x+30-30 \le 0-30[/tex] ... subtracting 30 from both sides

[tex]6x \le -30[/tex]

[tex]6x/6 \le -30/6[/tex] ... dividing both sides by 6

[tex]x \le -5[/tex]

The inequality sign does not flip because we are dividing both sides by a positive number.