This week we wrote the chapter 4 test as well as the midterm so we didn’t learn anything new except on Friday.

We started off with lesson 5.1 in the new unit and this was about representing basic inequalities:

 

For example:

We are given the inequality: x 0 and are told to graph it.  Since this is just a linear term (there are no square terms) we can graph it by plotting it on a number line. This represents our x-axis.

 

To graph it, we know that all of the numbers to the right of a specific point are considered “greater than” that particular number. Likewise, all numbers to the left of any specific value are known as “less than” that respective value.

We have 4 symbols to represent this:

means less than the indicated value.

means greater than the indicated value.

means less than or equal to the indicated value

means greater than or equal to the indicated value.

 

Graphically, we can represent these 4 statements with closed and open dots:

 

Closed dots for greater or equal to and less than or equal to:

 

And open dots for greater than or less than:

 

So now if we return to our problem, here is how we would represent it graphically:

We see the symbol  symbol after the x. Since we know that all of our points are less than or equal to 0, we will draw a closed dot on the indicated value of zero and draw the line to the left because its indicating all values less than 0.

 

We also learned how to solve an inequality using our algebra skills.

For example:

If we have 2x-3>11, here we just have to re-arrange the equation so that we can have x alone on one side:

We can add 3 to both sides:

2x>14

and then divide both sides by 2

x>7

and here we have our final answer. In this situation, all of the numbers greater than x are going to be valid in this inequality.