Question

please help!: write and solve an equation to find the length of each segment, AB=y-2,BC=y,AC=22 find AB and BC

Answer 1

Hi!
Firstly, AB + BC = AC. Imagining a picture might help.
But point "B" could be anywhere on that line. We don't know. Actually, it's y-2 away from point A, and y away from point C, but that'ts not intuitive, because we don't know "y".

We know that AB + BC = AC. By substituting each of AB, BC, and AC with their given equivalents, we get
(y-2) + y = 22

Now we can solve for "y", and the lengths "y-2" and "y" will be obvious.
So we start with
y - 2 + y = 22
If we do (add, subtract, multiply, divide) something to both sides, each side's quantity is changed, but they're both changed the same way. Since they were equal before, they'll be equal after. I just mention this because it means that we get a whole new equation, and it might be easier to work with.
I employ this technique to make new equations without certain problems. Like...

You saw the equation above. Here I change it by adding 2 to both sides. And here is the new equation.
y - 2 + 2 + y = 22 + 2
And here is that same equation, solved a little.
y + y = 24

Next algebraic move I'll pull: y + y is actually 2 times what y is. It's "2*y". Since y + y = 2*y, I can substitute in "2*y" for "y+y" - just because they're equal and I'm not changing the value of either side.
2*y = 24

Now I go back to what I did before; I'm gonna make a new equation. This time, it's value will be halved. I figure that if we divide "2*y" by "2", we get "y". Sounds good.
But I have to divide both sides by 2, or they won't be equal expressions anymore.
New equation:
y * 2 / 2 = 24 / 2
Solved:
y = 12

I hope you've learned how to do this!

To decide how to get a number away from a variable, look at what the number's doing to it. Then fight back.

2*y
If 2 is multiplying y, you divide by 2.

y/2
If 2 is dividing y, you multiply by 2.

y+2
If 2 is adding itself to y, you subtract it from y.

y-2
If 2 is subtracting itself from y, you add it to y.

Answer 2

Sorry for not finishing..
To find AB, which is y-2, you calculate y-2.
Since y = 12, y-2=12-2=10.

And BC is y, which is 12.

Double check!
AB + BC = 22
10 + 12 = 22
Well, we're not definately wrong! :)