What I learned about grade 9 solving equations

What is a fraction?

a fraction is actually a nice way of avoiding nasty divisions.

ex: $\frac{1}{3}$ = $1\div 3$

what are equivalent equations?

equivalent equations are math questions that equal the exact same number.

ex: $7$ = $7$

(Even though the next two don’t have the same numbers on both sides they can be simplified and you will see they are equal.)

ex: $3$ = $6\div 2$

ex: $2$ = $\frac {30}{5}-4$

How to solve equations with X

when you have an equation with X or another letter of the alphabet the equation wants you to find that variable.

To find the variable you need to get all the X on one side and all the other numbers on the other side then you need to flip, divide and/or multiply both sides until you get 1x and the numbers on the other side is the answer to X.

How do you move X and the other numbers from side to side?

You can move a number or variable from one side to the other by minusing it on both sides then you will have the opposite form of that number on the other side of the equation. By moving numbers from side to side you can simplify it into x=… and then you will have the answer.

ex: $2x+3$ = $3x-2$

$2x-2x+3$ = $3x-2x-2$

$3+2$ = $x-2+2$

$5$ = $x$

(That’s how its solved algebraically!)

Here’s another example on how to solve algebraically

$\frac {2(9x-2)}{3}$ = $3(x\cdot 3)-5x$

first you need to open the brackets

$\frac {18x-4}{3}$ = $3x\cdot 3-5x$

then you need to simplify ti enough so you can start moving all the X to one side and all of the numbers to the other side.

$18x-4$ = $9x\cdot 3-5x$

$18x-4$ = $27x-5x$

$18x-18x-4$ = $27x-5x-18x$

$-4$ = $4x$

then you divide both sides by 4 because you want to know the value of 1x and not 4x.

$-1$ = $x$

how to solve X with algebra tiles

With algebra tiles you can solve the question but more visually.

Here I’m going to solve $2x+2$ = $x-3$ with the help of algebra tiles.

Now we can clearly see that to isolate X we need to get rid of it from one of the sides. (The side with a bigger X is the best side to get all of the X on.)

By adding negative X on both sides we can make zero pairs to get rid of all of the X on the right and turn the left into 1x.

Now that we have all of the remaining X on one side we need to put all of the numbers on the other side to see what X is equivalent to.

Now we remove the zero pairs.

Now we can clearly see that X is equivalent to -5 and we can see if it’s correct by replacing all the X’s by -5 and see if we get an equivalent equation.

And as we can see here by replacing all of the X’s by -5 we got an equivalent equation which means we did all the steps right.

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