My favorite sport to watch is hockey (go Leafs go!). If you didn’t already know, in hockey, if a team scores 3 goals in one game it’s called getting a hat trick. This week I got the KA equivalent of a hat trick.

I’m happy to say I finished three units this week, Solving Equations & Inequalities, Working with Units, and Linear Equations & Graphs. To be fair, each unit was already ~50% finished before I started and they were essentially “refresher” units in the sense that I worked on all these types of questions in weeks past but, regardless, I’m still pleased with the progress I made.

In Solving Equations and Inequalities I worked through questions that asked me to solve linear equations and inequalities to find the value (i.e. the solution) of the unknown variable. This was good practice adding/subtracting/multiplying/dividing both sides of an equation/inequality to come up with the answer. A few things I learned/re-learned from this unit are:

• When solving a linear equation/inequality, if it is reduced to:
  • x = 5 (or any number), there is 1 solution (ex. 17z + 9 = 4z + 5),
  • 3 = 5, there are NO solutions (ex. 2x + 4 = 2x + 2),
  • 13 = 13, there are infinites solutions (ex. 24x + 80 = 24x + 80).
• When dividing both sides of an inequality by a negative number, you must flip the inequality.
  • Ex. 5x > 8x + 27 —> 5x – 8x > 27 —> -3x >27 —> -3x/-3 < 27/-3 —> x < -9

In this unit, I also worked on Compound Inequalities which asked me to represent two inequalities on a number line and essentially determine if they overlapped or not. If two inequalities overlap, you can say they have a common solution (i.e. they each have at least one value that is true for both inequalities).

The second unit I worked through, Working with Units, brought me back to working with rates and rate conversion. I was given questions which asked me to convert km/h to sec/min, kg to grams, liters to milliliters, etc. A few weeks ago I struggled with these types of questions but found this time through they weren’t nearly as difficult. I found the key to these multi-step rate conversion questions is simply to line the rates up properly when writing them down and then it’s easy to multiply across.

The final unit I finished, Linear Equations and Graphs, got me back into graphing linear equations. I did this by finding the X and Y intercepts and the slope (m). Again, I didn’t find these questions all that difficult this time through and had a pretty good recollection of the formulas I needed to use from a few weeks ago. The two key formulas I used in this unit were:

• y = mx + b
• m = (y[2] – y[1]) / (x[2] – x[1])

One thing I had to go back to double check was that when y = 0 the line on a graph is horizontal and m = 0 and if x = 0 the line a graph is vertical and m = undefined.

The next three units coming up are Forms of Linear Equations, Systems of Equations, and inequalities (Systems & Graphs). My hope is that I can finish all three units this week, however it will be difficult as I’m working this Friday which is typically one of my two days off. That said, I think if I grind through the first unit on Monday I can make it happen. Two hat tricks in a row would be pretty sweet.