Graph the inequality x ≤ -7.

Since it is  x  LESS than or EQUAL to  -7

  -7 should have a SOLID dot and the arrow should go away from -7 to the left (Less than -7)      A

 

x is BETWEEN -3 and +5   AND INCLUDES -3 (solid dot) but NOT 5 (hollow dot)       D

Something to know before we begin:

If a dot is CLOSED, then the inequality is an EQUAL inequality (\(\geq\) or \(\leq\)).

If a dot is OPEN, then the inequality is a NON-EQUAL inequality (\(<\) or \(>\)).

A good way to remember this is that you need to write more for both CLOSED dots and EQUAL inequalities.

 

Now, with this info, we can begin.

 

 

\(x\leq -7\) means that x is less than or equal to 7.

Since the inequality is indicating "less than," the arrow should point to the left side.

We can eliminate B and C.

Now, with the tips at the top of this response, we can find that the inequality is an EQUAL inequality, so the dot should be closed.

Therefore, the answer is A.

 

 

For the second one, since x is between two numbers, we know that it does not go on forever. We can eliminate B and C.

Can you solve it from there?

 

 

 

You are very welcome!

:P