# How to Solve any Algebraic Expression at KS3

June 23, 2020

The important thing for solving algebraic expressions, in other words, how to find the value of the variable in the equation, is to remember 2 key points

*(Let us consider the example ***11x + 2x ^{2} – 31 = 15x – x^{2} – 4x + 401**

*)*

- **1 ^{st} Key Point** –

*“Like terms”*– When we have an equation like our example, we need to make sure that our terms with common variables or constants are grouped together on the same side of the equation.

So, in our example we would group together our x^{2} terms (2x^{2} and -x^{2}), our x terms (11x, 15x and -4x) and our constants (-31 and 401). But this does not simply mean add them together, we need to remember our next key point…

- **2 ^{nd} Key Point** –

*“Change the side, change the sign”*– This saying is very useful in reminding us that when we move a term onto the other side of the equation we need to change its sign (positive or negative). This is because when grouping together terms they must be on the same side of the equation so that we can add or subtract them.

*Note: We move can move terms onto the other side because it represents the same information:*

** 5 - 3 = 2** and

*5 = 2 + 3*So, in our example **11x + 2x ^{2} – 31 = 15x – x^{2} – 4x + 401 **becomes

*11x -15x + 4x +**2x*^{2}+ x^{2}= 401 + 31*Note: It does not really matter what side we put our group terms on, but it generally does help to have our variables on one side and the constants on the other like we have done*

We can now simplify our equation

**11x – 15x + 4x = 0x**

**2x ^{2} + x^{2} = 3x^{2}**

**401 + 31 = 432**

Therefore

~~0x +~~ 3x^{2} = 432

*Note: An interesting thing to know is that with any equation we can do whatever we want to it, as long as we do it to both sides, and it will represent the same information. For example, we can multiply both sides by 3, minus 7 from both sides or square both sides.*

In our example we should divide both sides by 3 as we want to get x by itself. This makes

x^{2} = 144

Now we can finally square root both sides to find that

x = 12

This is a more advanced question in KS3 algebra but works for all forms of equations at this level. Here we found that when we simplified our equation, we got rid of our x term (11x – 15x + 4x = 0x). A KS3 level we are used to 1 variable and constants after we simplify like this example, but sometimes we will have the original 2 variables and the constant. We can get onto this in GCSE and is known as quadratic formulae…

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