Algebra and Other Stuff

Hey everybody!

So, tomorrow is our final quiz on this algebra unit for term 2! Hopefully everyone in FE8B has been studying hard - I know I have!
Some things that we have learned for the final quiz are doing 2 step equations, and then how to solve equations that have different terms in them. For example: when the variable is the numerator or denominator of a fraction, when there are variables on both sides of the equal sign, and when we have to break brackets with variables in them. Here are some examples of each.
When the variable is the numerator of a fraction:
x/2 + 3 = 7
x/2 + 3 - 3 = 7 - 3
x/2 = 4
2(x/2) = 4 (2)
x = 8
check:
(8)/2 + 3 = 7
4 + 3 = 7
7 = 7
-> In that equation, I first moved the whole integer (+3) from the left side to the right by undoing it on the left, then doing the same function to the right side. Then I multiplied the fraction by 2, as that was the denominator, and did the same to the other side. The two 2s cancel each other out, leaving me with x=8. Then, I checked and it worked out.

When the variable is the denominator:
4/x + 6 = 10
4/x +6 - 6 = 10 - 6
4/x = 4
x(4/x) = 4(x)
4 = 4x
4/4 = 4x/4
1 = x
check:
4/(1) + 6 = 10
4 + 6 = 10
10 = 10
-> In that equation, I did the same as in the previous. So in the 4th line I multiplied the 4/x by the denomitor (x) and did the same to the other side. The two x's cancel each other out on the left side, giving us 4=4x. Then we divide each side by 4 (the coefficient) so that we get 1=x.

When there are variables on both sides of the equation:
3x = 5 + 2x
3x - 2x = 5 + 2x - 2x
x = 5
check:
3(5) = 5 + 2(5)
15 = 5 + 10
15 = 15
-> In that, all we have to do is cancel the integer with the variable on one side, and do the same function to the other side. That's how we got 3x-2x on the left side.

Finally, when there are brackets to break:
2(3 + x) = 10
6 + 2x = 10
6 - 6 + 2x = 10 - 6
2x = 4
2x / 2 = 4 / 2
x = 2
check:
2(3 + 2) = 10
6 + 4 = 10
10 = 10
-> In that equation, to break brackets what you have to do is multiply the number outside the brackets by each of the ones inside the brackets separately. Then it is just like any of the equations above.

In Science we started a new unit on water systems. We learned about how most of our water on the earth is polluted, to deep to get, or is salt water. Did you know 97% of the Earth's water is salt water? I didn't know that before today. Anyways, I will report more on that next week as we get more into the unit.

Until next Wednesday,
-K