Algebra (Period 1)

MORE ON SOLVING EQUATIONS 3-3 to 3-5

Steps with Distributive Property
USUALLY you want to distribute first!!
(Unless the factor outside the ( ) can be divided out of BOTH SIDES PERFECTLY!!

5y -2(2y +8) = 16
5y -4y -16 = 16 {distribute accurately}
y - 16 = 16 { collect like terms}
y = 32 { solve by adding 16 to both sides!!}

-3(4 +3x) = -9
Wait you could distribute but if you divide both sides by -3
{the -3 goes into BOTH SIDES PERFECTLY}
you have 4 + 3x = 3
3x = -1 { subtract 4 from both sides}
x = -1/3 { Divide both sides by 3}

What if you have variables on BOTH SIDES of the equation?

Simplify each side of the equation first
THEN use the additive inverse property to move the variables to the other side, Usually we try to move the smaller coefficient to the larger because some times that avoids negative coefficients. But it is not always the case.

3y - 10 - y = -10y + 12
combine like terms
2y - 10 = -10y +12
In this case I would add 10y to both sides to get rid of a negative coefficient
12y - 10 = 12
Now add 10 to both sides
12y = 22
Now divide both sides by 12
y = 22/12 or y = 11/6