If I look at the middle table, my enlargement is a scale factor of 2. To enlarge my image, I multiplied the given information by two.

My reduction was a scale factor of 0.5. I reduced the given information my multiplying by 0.5.

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.

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

Patterns:

• 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.