A quiet week that pays off later. You learn to name the kind of number set you are working in, and you learn to rearrange an equation before you try to do anything with it. That second one is the real lesson. Most equations do not arrive in the shape you need. Getting y by itself first is not busywork, it is the move that makes graphing and substituting possible at all.
What you have to be able to do
Tell a finite set from an infinite one and use membership notation
Rearrange an equation into y-equals form before graphing or substituting
Set up and solve a percent word problem
The procedures
Rearranging before you graph
Get the y term alone on one side. Move everything else across.
Divide by whatever is multiplying y, and divide every term.
Now the equation is in a shape you can read a slope and an intercept from.
Percent word problems
Write the percent as a decimal. 30 percent becomes 0.30.
Translate the sentence directly: "of" means multiply, "is" means equals, and the unknown gets a letter.
Solve, then check the size of the answer against common sense.
Worked
WORKED
Rearrange 2x + 3y = 12 so it is ready to graph. Subtract 2x from both sides: 3y = −2x + 12. Divide every term by 3. ANSWER: y = −(23)x + 4
WORKED
Thirty percent of what number is 21? 0.30n = 21, so n = 21 ÷ 0.30. ANSWER: n = 70
Terms
Term
Meaning
finite set
a set you could finish counting
infinite set
a set that never runs out
element
a member of a set
Check yourself
1. Rearrange 4x + 2y = 10
2. Fifteen percent of 80 is what?
3. Is the set of whole numbers between 1 and 5 finite or infinite?
reveal answers
y = −2x + 5 · 12 · finite
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 15, sets, rearranging, and percent problemsalgebra 1 · oda