Graph the inequality -3 ≥ 2x + 3 > 7

Question

How do you graph on a line??

Answer 1

You want to simply the expression so that all 'like terms' are combined and all numbers have been reduced (if possible). If the expression said -3 > 2x +3, you would subtract 3 on both sides to read -6 > 2x, and then you would divide by 2, right? Your answer would read: -3 > x.

But that's what you would do if that > 7 wasn't there. With the > 7 on the right side, you're going to do everything you just did in the example above (subtract 3, divide by 2), but you're going to do it on both sides of the expression.

We just did the left side, with the -3. Now we'll work with the > 7 (the right side): subtract 3, so that you have 2x > 4, then divide by 2 to get x > 2.

We have both sides of the inequality now: (-3 > x) and (x > 2). So let's smash it together: -3 > x > 2.

That's your simplified expression.

TO GRAPH THIS:

Your expression says that your x-values are between -3 and 2. This means that your graph is going to cover the space between -3 and 2 (including those values, because your expression uses "or equal to"). If you are working with line graphs, this is an example of what you will draw: a line, with hashmarks, going from maybe -5 to positive 5. At -3 and 2, you will draw "closed circles" and you will draw a line connecting these two circles.

Any questions, let me know!