Understanding Maths and Equalities

[Gaeas_Freikugel]

Hello,

I’ve started looking through this course as Stephen from the C++ beginners course has started looking into vectors, and understandably he didn’t go into detail as that’s not the point of the course. So I reattempted the Math course (accessed twice before and stopped in the Algebra & Equations section’s first quiz). I decided to go through it until the Vector’s section as even when I went through Stephen’s course on C++ some details he went over I wasn’t following mathematically on calculating movement/gravity, etc.

I seem to be struggling with Gary’s detailed information on flipping parts of the equation to find the missing value/variable. e.g. 10 => -2x + 5 Is there a methodology in maths where you can flip parts of the equation I’m not familiar with? I didn’t understand why moving ‘+5’ became -5 + 10 => -2x. Same goes for moments later where the equation becomes 5/-2 <= x. Also noticed the sign for -2 doesn’t become inverted unlike the + 5 from the first equation.

So far I feel it’s going over my head. Although the first section is useful as a lot of segments I was either weak at before or had limited knowledge, even if still abstract in it’s utility for me currently. However it seems some concepts being discussed are at a skill level I’m not grasping or I’m missing key points that allow me to follow along.

Should I be expecting this to make sense this early in the course or does it come into play later?

Thank you in advance for helping and thanks for reading.

[RayMobula]

Hello there,
He asks to isolate for x, or? (Haven’t done the course)

In math you must do the same operation on both sides

To get the 5 to the other side, you can write -5 on both sides
10 => -2x + 5
-5+10 => -2x + 5 - 5

Which then becomes
5 => -2x

^^^ btw, the -5 didn’t become inverted, you solved -5 + 10 = 5.

Next, to isolate x you need to get rid of 2. Divide both sides by 2
5/2 => -2x / 2

Which is becomes
5/2 => -1x / 1

Resulting in
5/2 => -x

Since x must be positive, by convention, you need to multiply both sides by (-1)
5/2 * (-1) => -x * (-1)

This results in
-5/2 <= x

Keep in mind when you multiply or divide with a negative number, in inequality sign flips.
Of course, you could have divided by directly (-2).

Finally, you’d write this as. (don’t forget to flip the inequality sign)
x => -5/2

Hope this makes sense and helps.

Have you checked Khan Academy? It’s a useful resource too.

Cheers,
Ray

[Gaeas_Freikugel]

Hello Ray,

Thank you for this, it makes more sense with how it’s detailed. Gary didn’t show doing the same operations you showed (see image and right hand side), which is probably where my confusion is coming from.

I was looking at Khan Academy moments ago and I’ll probably supplement the course with that. As I feel I’m not on the same level as what’s discussed in the course and it’s what scared me off the first two times when I went through it.

Yes he asks to isolate x to figure out what it would be in context for a variable of a game, for example a rocket game which burns fuel based on time, maximum fuel, current fuel and the burn rate of that fuel.

[beegeedee]

Hi, I’m coming late to this.

Basically you’re keeping both sides of the equation balanced.
So…
10= -2x + 5

you want to cancel the 5 so subtract 5, but to balance you do from both sides

10 - 5 = -2x + 5 - 5
10 - 5 = -2x
5 = -2x

Next, you want to cancel out the -2x so you have just x. You do this by dividing both sides by -2
5/-2 = -2x / -2
so, -2.5 = x

It’s about maintaining balance.

Another example, a bit more complicated…ish

x^2 - 5 = 4

In this case, you want x, and so you need to perform a square root on both sides but before that, add 5 to both.

x^2 - 5 + 5 = 4 + 5
x^2 = 9
Square root now
x = 3

I hope this makes sense.

[Gaeas_Freikugel]

Hello beegeedee,

Appreciate your detailed rundown as well. That’s what I was missing to find x, the balancing of each side of the equation.

I’ll still review from another source to strengthen my knowledge as I’m either very rusty or missing key points to calculate or break down equations.

Thank you both for taking the time to explain this for me.