When graphing inequalities, if the sign is greater than or less than, you leave the circle open. If the sign is greater than or equal to or less than or equal to, then you would have a closed circle on the number.
The answer would be #x>3 and x<7# because the first step in this problem is to solve the inequalities. You would do this one at a time, starting with the first inequality. #2x>−6# You would solve this by simply dividing #6# by #2#. So, the answer to this inequality would be #x>3#.
The second inequality is #x-4<3#.. You would simply add four to three and get #7#. The inequality is now #x<7#. Now, we graph.
Simply draw a number line and as I said before, put an open circle on #3# and #7#. Then, you shade in the space between them. Whenever graphing compound inequalities, there are two rules. When the inequalities are connected with and or written as #3>x<4#, the inequalities meet in the middle. When they are connected with or, the go in opposite directions.
