What is a linear equation? A linear equation is an equation between 2 variables that when plotted on a graph, gives a straight line. It has an equals sign in between the 2 halves of the equation to join it together. The 2 variables can be in fraction form, decimal, integer or whole number. If you are using fractions, the easiest way to simplify the equation is to find a common denominator, which Is a number that all the denominators have in comon. For example, ‘1/3x+2/6=8/12x+1/3’, would have a CD of 12. Changing the bottom denominator means you also have to change the top number, and multiply it by whatever you multiplied the denominator by. ‘4/12x+4/12=8/12x+4/12’.
Linear equations can also be equivalent expressions. These are algebraic expressions that are made equal by changing the values of the numbers. An equivalent expression of 4x+3=-6x-2 would be 4x+3=2(3x+1) and 10x+5=0.
How can equations be modelled? They can be modelled using algebra tiles in paper form or drawn on. The dark tiles represent positive integers, and the white or non-coloured tiles represent negative integers. The dark rectangular tiles are used for 1x, and the smaller cubes are used for 1. The white rectangular tiles are used for -1x and the smaller cubes are used for -1.
Equations can be solved visually many ways. One way is to use algebra tiles, and another way is to draw the tiles onto the paper on the correct formatting of the equation.
One way you can solve equations algebraically is by grouping the like terms together and solving it from there. The distributive method is when you have a whole number and you have to distribute it to numbers inside the brackets. An easy way to verify the solution is to work the question backwards and to pretend like you don’t know what x is. You can also find the zero pairs if you have ‘3x-2=4x+3’, the first zero pair would be ‘-3x’, which cancels out ‘+3x’. The equation would then be turned into ‘-2=1x+3’ and the next zero pair would be ‘-3’. Thus, the simplified equation would be ‘-5=1x’.
In the expression ‘4x-7=5’, 4 would be the coefficient, since it is the value that comes before the variable, which is x. The constant term would be -7 and =5, since those are the things that do not change. The operator is subtraction. A solution is having the ability to check that no matter what you are using as x, 4x-7 will always equal to 5.
Here, for this equation below, I first started by making zero pairs with the negative 4x by adding positive 4x. After that, I added 8 to make zero pairs with the 8. After that was finished, I ended up with ‘+10=10x’, and if I divide 10 by 10x, then I get 1x=1. I also solved It with algebra tiles.
The picture above is me solving an equation using the regular strategy of how I normally solve it. The picture below is me explaining how to solve it with algebra tiles.
