Chapter+Two


 * Chapter Two

Sec 2.1 **
 * Variables vs. Constants
 * Constants are numbers that don’t change. So if you have 6 + 4, both the six and the four are constant, because 6 will always be 6 and four will always be four.
 * Variables are represented by symbols or letters and it indicates that we don’t know what the value is, or it could be any value, or it might have the value entered later. So in the expression 6 + X, we aren’t sure what X is, so it is called a variable because it can vary, opposite of constant.
 * Expressions (c+5 or 3x-2) An expression represents a value, but sometimes we don’t know what the value is because it includes a variable.
 * Coefficients are the numbers in front of the variable, or how many of those variables there are. So in the expression 6X + 3, the coefficient is 6.
 * Expressions with two variables (x+y=?) In order to figure this out, you have to figure out what one of the variables is equal to, then plug that in and solve. There may be many solutions that would work for this expression, but if you nail one of the variables done, it really limits what the other one can be.
 * Exponents with variables as bases, such as [[image:file:///C:%5CDOCUME%7E1%5Cstaff%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image002.gif width="36" height="16"]]
 * Sec 2.2 **
 * Simplify expressions by combining like terms.
 * A like term has the exact same variables and exponents.
 * 6x and 6y are not like terms
 * 6x2 and 6x3 are not like terms
 * 4x2y and 3x2y are like terms
 * 3x + 4x = 7x
 * This is like reverse distributive property (3∙x + 4∙x) = x(3+4)
 * That means you add the coefficients, but not the variables.
 * Think of it as having 3 bags of oranges and adding 4 bags of oranges, giving you 7 bags of oranges.
 * You can’t add or subtract unlike terms (x+5) (but you can multiply them)
 * S implify expressions means you add the like terms. You may not ever get to an answer that is just a number, but if all of the like terms have been combined, it is simplified.
 * Sec 2.3**
 * Equations are math problems with an equals sign. Whatever is on the left side equals whatever is on the right side, even if they don’t look alike – their values are equal.
 * In the equation: C + 10 = 15, the answer is C = 5 5 is called a solution. Whatever number(s) could be substituted for the variable is called the solution. If no number would work to make the equation true, it means there is “no solution”.
 * Addition property of equality says that if you add the same amount to both sides of the equals sign, the equation will still be true. Adding something, like 6 to both sides, might make the equation easier to solve.
 * C-2=10 In this case, add 2 to both sides to get C = 12
 * C+9=5 (adding an opposite) Add -9 to both sides to get C = -4
 * Simplify before solving. Combine like terms //before// you add or subtract numbers (or variables) from either side.
 * Sec 2.4**
 * Division property of equality – You can also divide both sides by the same value to simplify. However, it means that you have to divide all of the left side and all of the right side by the same thing.
 * 6x = 30 Divide both sides by 6 to get X = 5
 * Simplify before solving. Combine like terms on both sides before dividing anything.
 * Don’t leave a negative variable ( -x = 4 ) In this case multiply both sides by -1 or divide both sides by -1. Either way, you will get X = 4
 * Sec 2.5**
 * Solving two-step equations
 * Two-step equations usually involve both adding something to both sides, then dividing both sides by some value.
 * Steps on page 129
 * 5m + 1 = 16 – Add a -1 to both sides, then divide both sides by 5
 * Check your answer by substitution. When you get a solution, plug that number back into the original problem and see if both sides are really equal. If they aren’t, you probably did something wrong when you solved the problem.
 * 2x – 2 = 5x – 11 -- In this case, you need to add a number to both sides (probably +11), then add a variable to both sides (probably -2x). At that point you should have 9 = 3x. Then divide by 3 on both sides to get 3 = X which is the same as X = 3.
 * -6 = 3(y-2) -- If you see something like this, do the distributive property first, then continue with the solution as normal.