Algebra Period 4

Solving Equations 1-7

Equations use an = sign to show that two expressions are equivalent
Equations can be true, false, or open
If an equation is NUMERICAL (numbers), it must be either TRUE or FALSE:
3 + 5 = 8 is TRUE
3 + 5 = 9 is FALSE
If an equation is ALGEBRAIC (variables), it is OPEN for discussion
(it all depends on what the variable is!)
y + 4 = 10 is OPEN

SOLUTION = answer
REPLACEMENT SET: The set of answers that you have to choose from for the answer.
SOLUTION SET: All the answers that make a statement true.
{ } set symbol
EXAMPLE: Solve y + 4 = 10 for the replacement set {2, 6, 10}
Substitute each element of the replacement set into the equation to see which one(s) work
Only 6 works, so only 6 is a true solution
The solution set is {6}
Note that if the replacement set was {2, 7, 10} for y + 4 = 10, then the solution set would be the NULL SET which means the solution does not exist in the replacement set.
The symbol for the null set is a zero with a line through it.

Equations must always be in balance.
GOLDEN RULE: WHATEVER YOU DO TO ONE SIDE OF AN EQUATION, YOU MUST DO TO THE OTHER SIDE or you'll be out of balance.
One way they might ask this question on the STAR Test is to ask:
What was done to the first equation to get the second?
EXAMPLE: 3x - 5 = 12 and 9x - 15 = 36
The first equation was multiplied by 3 to get to the second equation so they are equivalent.