Can someone explain inverse operations to me?
Our teacher was off today and I just want to understand.
So, I get simple stuff like adding and subtracting but, like, for example if we were to make x the subject in this example (m=yx)how were we to do it?
More example I don't understand:
Make x the subject:
Y=s²-y
Make p the subject
W=p/b - t
Please help me!
in m=yx
to "make x the subject" means to solve for x
so in yx, the x is multiplied by y, the inverse operation of multiplication is division, so ...
I will divide both sides of the equation by y
m = yx -----> m/y = yx/y
m/y = x <---- that's all there is to it!
in W=p/b - t
the last thing they did was to subtract t, so the first thing I will do to reverse the process is
to add t
W=p/b - t ------> W+t = p/b - t + t
W+t = p/b
p is divided by b, so I will do the inverse of division which is multiplication, then
(W+t)*b = p/b * b
b(W+t) = p , all done!
remember the inverse of addition is subtraction, the inverse of multiplication is division,
the inverse of taking the square root is squaring, etc.
Inverse operations are mathematical operations that "undo" each other. They allow you to isolate a variable in an equation by performing the opposite operation to both sides of the equation.
To make x the subject in the equation m = yx, you need to isolate x on one side of the equation. Here's how:
1. Start with the equation: m = yx.
2. Divide both sides of the equation by y: m/y = yx/y.
3. The y's on the right side cancel out, leaving you with: m/y = x.
4. To make x the subject, you can rewrite the equation as: x = m/y.
Now let's go through the other examples you provided:
1. Make x the subject: Y = s² - y.
- Start with the equation: Y = s² - y.
- Add y to both sides of the equation: Y + y = s² - y + y.
- Combine like terms: Y + y = s².
- Subtract Y from both sides of the equation: Y + y - Y = s² - Y.
- Simplify: y = s² - Y.
- Rearrange the equation with x as the subject: x = s² - Y.
2. Make p the subject: W = p/b - t.
- Start with the equation: W = p/b - t.
- Add t to both sides of the equation: W + t = p/b - t + t.
- Combine like terms: W + t = p/b.
- Multiply both sides of the equation by b: (W + t) * b = p/b * b.
- Simplify: b(W + t) = p.
- Divide both sides of the equation by b: [b(W + t)] / b = p / b.
- Simplify: W + t = p/b.
- Rearrange the equation with p as the subject: p = Wb + tb.
Remember, the key is to perform the opposite operation to isolate the variable you want to make the subject. In these examples, we used addition, subtraction, multiplication, and division as inverse operations.