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If you do algebra, the best way is to substitue all the numbers you find back in.

5x+7=20

20-7=15

5x=15

x=3?

3x5+7=20?

15+7=22 not 20 so x=/=3 so somewhere i went wrong.

Sometimes, doing a question a number of times can help check for errors. Say i had a binomial expantion. I would do it at least twice to make sure all the answers I got were the same.

You can also rearrange an answer to see if it still works and also do some question backwards to see if you get the same start.

34x29-12=972?

972 +12 = 984

984/29=33.586

Somewhere i went wrong.

Dont forget to reverse bidmas/bodmas/pidmas or whatever you call it when reversing a calculation.

If its done on a calculator, you can input the question in a number of times to make sure you didn't press a wrong button.

A constant term is a term that does not change, no matter what numbers are substituted in. 7x is not a constant variable because if x=2 then 7x=14. 2x^2 is not constant because if x=2, then 2x^2=8

The only term in this that does not change at all is 17, because it has no variable attached.

The formula for the area of a triangle is base x height x 0.5.

We can use any size base and then use algebra to find out how high the triangle should be.

Base 6

Height x

$${\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\times\,}}{\mathtt{0.5}} = {\mathtt{25}} \Rightarrow {\mathtt{x}} = {\frac{{\mathtt{25}}}{{\mathtt{3}}}} \Rightarrow {\mathtt{x}} = {\mathtt{8.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

Now we know that a triangle with area 25 and base 6cm is 8.3cm high.

You can replace the height and base number with any real positive number.

Now you have 3 points. The two points and the edges of the base line, and at the top of the height line. Now just join them up to get a triangle.

Is there a picture to go with this?

A square root is a mathematical operation where you find two of the same numbers which multiply together to give the number you are square rooting.

Example 1:

The square root of 16 is 4 and -4 because 4x4 is 16 and -4x-4 is 16.

Because the square root of 16 is an integer (whole number), it is a square number. 9,49,25,36 are all examples of square numbers.

Example 2:

The square root of a non square number will be a decimal. The most noteable example of this is root 2, which is an irrational number (a number that does not terminate)

Example 3: 

The square root of a negative number is impossible to do normally because to get a negative number by multiplication requires a negative and a positive number, meaning that the 2 numbers are not equal so you can't have a negative square root. Normally. This is where the complex number i comes in. i^2 = -1. Using i allows you to get a answer for negative numbers.

root -16 = 4i

root -36 = 6i

Deep inside, we're all Beyoncé.

>.>

When increasing a number by a percentage, you essentially find 100% + the percentage. In this case, 100%+60%=160%. As a decimal, this would be 1.6.

So

$${\mathtt{700}}{\mathtt{\,\times\,}}{\mathtt{1.6}} = {\mathtt{1\,120}}$$

This is 700 increased by 60%

When you decrease a number by a percentage, you are finding 100%-percentage decrease. In this case 100%-60%=40%. As a decimal this would be 0.4

So

$${\mathtt{1\,120}}{\mathtt{\,\times\,}}{\mathtt{0.4}} = {\mathtt{448}}$$

$${\frac{{\mathtt{y}}}{-{\mathtt{8}}}}{\mathtt{\,\times\,}}-{\mathtt{8}} = {\mathtt{\,-\,}}{\frac{{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{y}}}{-{\mathtt{8}}}}$$ then times both numbers by -1 to get $${\frac{{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{y}}}{{\mathtt{8}}}}$$.

Then cancel the 8 to get y

$${\mathtt{4}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)$$ is the same as $${\frac{{\mathtt{4}}}{{\mathtt{1}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)$$.

You multiply the top numbers together and the bottom numbers together, so its $${\frac{{\mathtt{12}}}{{\mathtt{5}}}}$$

First, make the two fractions have equal demoninators, so find a number they are both a multiple of. The lowest is 42, so

4/7 times 6 top and bottom = 24/42

1/6 times 7 top and bottom = 7/42

now take 7/42 from 24/42 to get 17/42.

Next take the 2 from 4 to get 2. Put it back together to get $${\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{17}}}{{\mathtt{42}}}}$$