Question

Choose the correct description of the graph of the inequality -6x 30.

Open circle on 5, shading to the left.

Closed circle on 5, shading to the left.

Open circle on -5, shading to the right.

Closed circle on -5, shading to the right.

Answer 1

someone please help

Answer 2

You'll need to share with us what the inequality symbol is.

-6x ??? 30

But basically, solve just like you would an Equality, with one exception: when you MULTIPLY or DIVIDE by a NEGATIVE number (as you have to do here) you have to flip the direction of the inequality.

The only other part you need to know is that, if it is a STRICT inequality (> or <), then the solution set will NOT INCLUDE the endpoint - hence, the graph gets an OPEN CIRCLE at the endpoint.

If it is a WEAK inequality (\(\ge\), \(\le\)), then the solution set DOES include the endpoint - hence, the graph gets a CLOSED circle.

Answer 3

Eg, if I have:

\(x \ge3\) , 3 IS in that solution set (since it makes the inequality true). So I have a closed circle on 3, and extend to all x's greater than 3, so to the right/

If I have:
\(x >3\) it is almost the same, except with an open circle on 3 (since 3 does NOT make the inequality true).

For \(x \le3\) or \(x < 3\), same as above, except the solution set includes all x's LESS THAN 3 so the graph extends to the left.

Answer 4

≤ thats the inequality symbol

Answer 5

I thought it would the last one closed circle on -5, shading to the right.

Answer 6

\(\Large -6x \le 30\)

So divide by -6 (and hence flip the inequality):
\(\Large x \ge -5\)

So yes, you're exactly right. :)

Answer 7

Thank you so much

Answer 8

you're welcome. :)