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Multi-Step Equations!
"Inverse Operations" vs "Collecting Like Terms"
A NEW WAY to think about Isolating the Variable! Moving Terms...
We want all the variable terms on one side, and the constants on the other.
get rid of brackets, if there are any. Distributive property
collect like terms (now or after)
move all the variable terms to one side, constants to the other...
collect like terms, simplify each side...
Solve.
Moving Terms
When we isolate the variable by using inverse operations, that means what we do to one side we do to the other. You should already know this!
BUT a shorter way to think about what we SEE is...a term MOVES across the equal sign and changes it's sign from a + term to a - term, and vice versa!
Think about it...
Examples:
x - 23 = 8
If we take the -23 term and move it across the equal sign, it becomes +23
On the left this is the WHY IT LOOKS THAT WAY!
Here are some other examples...
The NEW RULE!
*We can move terms across the equal sign as long as we change the sign of that term!
*We collect like terms by sending all x-terms to one side, and constant (regular numbers) to the other!
*sometimes we need to "unlock the variable" with distributive property
*sometimes we need to deal with fractions first
*sometimes we need to put like terms together...
Fractions application...
a. need common denominators (use equivalent fractions)
b. terms with variables on same side, constant terms to the other
c. simplify and solve
common denominators for fractions...review
To solve these equations, we need to use the same ideas behind fractions with uncommon denominators!
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