I’m interested for personal reasons on how these mathematical operations work. I know they’re quite simple, but I never quite understood them, so it’s something that got stuck with me. Any explanations are welcome!
In: 4
You mean pre-Algebra/Algreba I equations of lines, or solving systems of equations (generally Algebra II)?
A linear equation is just that, an equation for a line.
You the value at an unknown/variable point on the line, x.
You have the value of how drastic or not it changes between positions, slope (m).
You have the starting value (at x=0), the y-intercept (b).
You have the output, y.
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**Example**
y=2x+3
This means that no matter what number x is, you double it and add 3 to get the result/output.
If x = 4, the you have 2*4+3 = 8+3 = 11.
X number line is usually horizontal.
Y number line is usually vertical.
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**Example problem**
3=5x+13
We need to find what number, when multiple by 5 and then adding 13, equals 3. This obviously needs to be a negative value.
5x would need to be -10 (13-10=3)
x then needs to be -2 (-2*5=-10)
Plug it in to check:
3=5(-2)+13
3=-10+13
3=3
It works.
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**Example problem #2**
3x+5 -2x = 6x-10
We don’t really care about the line, mores just x.
So what number if you multiply it by 3, add 5, and then subtract 2 of itself is the same as doing 6 multiples of it minus 10?
On the left had side it can be rearrange:
3x-2x+5=6x-10
Then simplified:
x+5=6x-10
So, if adding 5 to it is the same as multiply by 6 and minus 10, that means x itself is equal to 6 multiples of it self – 15.
x=6x-15
That means 5 multiples instead of 6 would not equal anything.
0=5x-15
This means 5 multiples of x cancels with subtracting 15, so it equals 15.
15=5x
3=x
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