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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Integers and Substitutions

Commutative properties a + b = b+ a

o If the largest number

• 2 + 4 = 6
• -6 -4 = 10

o Use your math number sense in order to deal with questions with only 2 terms Look at the terms and find the largest value. Whatever sign is of that term will be the value of the answer(ie positive or negative )

o For questions with multiple terms move one term at a time or a more risky way is to group terms…problems with this is of replacing the signs properly

## Â· When terms have multiply Signs

o There is a difference of a subtraction sign and a negation sign.

o An equation cannot have two signs ( + , - ) side-by-side. We must change the signs so that there is only one sign between them. There are some simple rules that we must follow

o Two minus’s become a plus

o Two plus’s become a plus

o One minus and one plus becomes a minus

• Ex - 20 - (-5) = -20 + 5 = -15
• Ex 7 + (+11) = 18
• Ex -4 - (-7) = -4 + 7 = 3

o This can also be done while using a number line

## Â· Multiplying and Dividing

o A negative times a negative gives a positive, a positive times a positive gives a positive, while a negative times a positive gives a negative. If they are both the same then positive, but if they are different then negative. If they are an even number of negatives then it will be positive, but if there are an odd number of negatives, then it will be negative.

o After the operation(s) if there is an even number of negative signs the answer is positive (or if all positive no worries)

o if there is an odd number of negative signs then the answer is negative

## Substitution

Â· The act of replacing an unknown with a known value.

o 5x 2 - 7y when x is 2 and y is 7

o when we replace an unknown with a value we put the new quantity in with brackets. This way we can show others what values we have replaced.

o Once all unknowns are replaced with given information we follow normal BEDMAS rules.

Â· Sometimes only some of the variables are accounted for. So we only replace those that we know. We cannot replace or get rid of variables.