What I Have Learned About Grade.9 Linear Inequalities

What is a Linear Inequality?

  • A linear inequality is an equation that involves linear functions. An equation also includes one symbol of inequality:
  • < is less than
  • > is greater than
  • ≤ is less than or equal to
  • ≥ is greater than or equal to
  • ≠ is not equal to
  • = is equal to
  • A linear inequality ressembles just like the linear equations from the last unit, except with an inequality symbol to replace the equal sign.

What do these Equations Mean?

  • If we were to write “x<4”, that would be that a number is less than four. Same goes for “x>4”, which would mean that a number is greater than four.
  • If we write “x≤4” that would mean that a number is less or equal to four. Same goes for “x≥4”, which would mean that a number is greater or equal to four.

How do you Graph a Linear Inequality?

  • When graphing linear inequalities on number lines, we use different types of dots to identify the inequality sign. if it’s an open dot, we use those for equations that contain less or greater signs. If it’s a closed dot, we use those for equations that contain less or equal to, and greater or equal to signs.

Here are some examples of linear inequalities plotted onto graphs:

(Graph 1: x<-2, Graph 2: x≤-2, Graph 3: x>-2, Graph 4: x≥-2)

How do you Solve Linear Inequalities?

  • Solving linear inequality equations is just like solving normal linear equations,
  • One thing that always helps me is to remember is

Best: Brackets

Friends: Fractions

Share: Sort

Desserts: Divide

These will help you remember what to do first when you are solving your equation.

  • Here is an example of the steps of solving the linear inequality equation “2x+4>3x+1”..
  • If an answer to an inequality equation is negative, you have to switch the sign to the opposite sign.


Solving Linear Equations

What is a Linear Equation?

  • A linear equation is an equation between two variables that gives a straight line when plotted on a graph.
  • Here are 2 simple examples of linear equations:   5x=6+3y       or     y=2x+1
  • Here is an example of a linear equation that has been plotted on a graph:

  •  Linear equations can contain variables that are whole numbers, integers, decimals and fractions. When dealing with linear equations that have fractions, the best way to solve it is to find a common denominator.

How can Equations be Modelled Using Algebra Tiles?

If you don’t have algebra tiles you can always draw out and solve the equation by drawing the tiles on paper. I did not have tiles so below I visually represented how I solved the linear equation.

  • When using algebra tiles, coloured tiles are positive integers and non-coloured tiles (white tiles) are negative integers.
  • Larger coloured rectangular tiles are used as 1x and the smaller coloured squares are used for 1.
  • Larger non-coloured rectangular tiles are used as negative 1x and the smaller non-coloured squares are used for negative 1.
  • See photo below:

This is an example of how I visually solved the equation below. I drew it out using algebra tiles.

How to Solve Equations Algebraically?

To solve the following simple algebraic equation I have get x all by itself. We call that isolating the variable.

If you have the equation:      2x+3=7

  • I want to get x alone. The first step would be to get rid of the +3 by subtracting 3 (this cancels each other out). I remember that what I do to one side of the equation, I have to do to other so I subtract 3 from 7. Now, I’m left with 2x= 4
  • to isolate the x I divide 2 by 2 to cancel each other out (which leaves me with x on its’ own). What I do to one side, I do to the other so I divide 4 by 2 and I get the answer x=2


What I Know About Grade Nine Linear Relations


  • A pattern is a repeated design that can increase or decrease the quantity of objects in each image.

  • This is an example of a linear pattern. You can see how the quantity of squares increases in each step.
  • A linear pattern is that if you plotted the information of the pattern onto a graph and the plotted points make a pattern, then the coordinates of each point may have the same relationship between the x and y values.
  •  Here is a T-chart that is made from the information included in the pattern above. If you look at the T-chart, you will notice that the numbers in the white column increase by four each time. This is a good thing to notice, as it will help you with the questions to come.

Linear Relation Rules:

  • A linear relation is a relationship between two products, that if plotted on a graph, it would make a straight line.
  • A linear rule is a algebraic expression that is used to demonstrate how to get the output Y-values for a given set of input X-values. This rule will help us determine what the rest of the pattern would be without even looking at the image! It would also help us know where to successfully plot the information onto a graph.
  • Going back to the information on the given T-chart above, we know that the number of squares goes up by four each time.
  • Let’s think that the grey column is also named “X”, and the white column is also named “Y”.  We would write “4x” to represent the X-value increasing my four, each step.
  • (4)(1) would not bring us to 6. Now it is time for you to figure out whether you should add of subtract to find the answer given in the “Y” column.
  • Now we know that the rule would be 4x+2

Plotting Points on a Graph:

  • Plotting points on a graph is simple. A graph is basically a horizontal number line (x-axis), crossing through a vertical number line (y-axis).
  • Let’s say that we had a T-chart that represented the rule “2x+1”.
  • We will use this information to plot our dots successfully onto our graph.
  • If you remember when I said that the grey column is named “X” and the white column is named “Y”, you will place the dot where 1 on the x-axis and 3 on the y-axis meets in the middle.
  • You will continue that by using the rest of the information in the T-chart and you will begin to notice that plotted dots create a straight line that will run through your graph.

ADL Community Connections Interview

Mme. Homeniuk

French Immersion Teacher – Grade 5/6

I chose to interview Natasha because she works with my mom at her school. Ever since I was little, I have always wanted to become a teacher when I grew up. I love working with children and think that teaching would be the best choice for me. I would like to work at the elementary level and even become a French immersion teacher.

I have learned from this interview that this is a job that requires a lot of responsibility and patience, but is a beautiful career because you get to make connections with your students and are able watch your students grow and become amazing people in the future.



  1. I am passionate about being a teacher because I love being a part of child’s growth and success. I love learning myself, and being a teacher is all about learning new things all of the time.


2.It takes a lot of schooling and post secondary education to become a teacher. I spent time being a TOC before I landed a full time position and the first few years of being a teacher is not easy. There is a lot time spent planning, prepping, assessing, conferencing, organizing, collaborating and providing feedback. Some years are harder than others.


  1. For someone who is interested in becoming a teacher I would tell them that they are choosing a profession that doesn’t allow for you to clock out when the workday is done. Be prepared to work very hard! However, it’s also the most rewarding profession to be in. You get to work with other awesome teachers and the best part is making connections with your students. There is nothing better than seeing your students grow and learn.

  1. Yes I would be open to further contact.


(own question) What is your favourite part of the job? I have a few favourite parts. I love working with other teachers. The teachers at my school are great and we collaborate a lot on ideas.  I love it when my ex students come back to see me! There’s no better feeling when they come for a visit and to say they enjoyed my class. And obviously my favourite part of the job is having a close connection with my students.


(own question) How many years does it take to become a teacher?

I did the PDP program at SFU after I got my degree. I also went back to university to get my 2 year 5+15 graduate diploma.  Some people go to UBC to do their teacher training, others have gone to UVIC.


Sites for pictures:



Solution Fluency Project – Kits for Kids

Define: All around the world, children, adults and families live in poverty. Approximately 1.3 billion people live in conditions of extreme poverty today. This is a big problem in our society. Many people around the world do not have access to the amenities and objects that we take for granted. It’s sad to think that there are children in our world that do not have access to a tooth brush or even a trusty pair of socks. Yes, there are organizations out there, already working on helping people who live in poverty, but the thing that makes us unique, is that we are children taking a stand and making it our mission to help other kids living in poverty. They say that children are the future, let’s help make the future bright an help the children of our world.


Dream: Our plan is to make a package, full of necessities like canned food, small clothing items, toiletries, etc. We are going to start off by creating one packages for one child and send it to a girl in Columbia. Once we know that our package was successfully created and sent, we will start to take our idea further and hopefully create many more packages for children in need, around the world.


Deliver: We are planning on placing all the items that we collected for the package and place them in a box to keep the items safe and unharmed. Then, we are hoping that the package will get hand-delivered to the child that we are giving the package to. We will not be there to deliver it, but we will be there in spirit and we will hope that she will like the package!


Debrief: We are proud that we have been able to think of an idea of how we could help our planet and actually create it! From the beginning, we wanted to fundraise to raise money for the packages and create several packages to give to several kids. Yet, due to our lack of time to fundraise and the amount of money that it would cost to create several packages without being able to fundraise, we decided to start with one package and go from there. I believe that all of us would’ve liked to send more packages then to just one, but we know that if we keep our dream alive and work hard to reach our goal, it will be some day possible. This project has really inspired all of us in our group to help others in our world. No matter how old or how far away you are, there is nothing stopping you from helping others.


Modeling Mitosis

1. Prophase. In this step, the nuclear membrane has dissolved and spindle fibres have begun to attach to the chromosomes and pull the fibres. The fibres attach onto the centromere, which acts like a belt that holds the two chromatids together.

2. Metaphase. In this phase, the spindle fibres have brought the chromosomes into the middle of the cell to for a straight line right down the center of the cell.

3. Anaphase. In this step, the spindle fibres have pulled the chromatids appart from each other and have dragged them to opposite sides of the cell. The cell begins to stretch and split.

4. Telophase. In this phase, the cell has split into two new cells and two new nucleuses have formed in each new cell. The chromatids that were split appart are now inside the new nucleuses.