Question 244891
PROBLEM NUMBER 1


3(x+2)-(3x+6)=0


simplify by removing parentheses to get:


3x + 6 - 3x - 6 = 0


combine like terms to get:


0 = 0


this is an identity equation.


since x dropped out of the equation and the equation is true (0 does equal 0) then x can be any value.


try x = 3


you get:


3(x+2)-(3x+6)=0 becomes:


3(3+2) - (9+6) = 0 becomes:


3*5 - 15 = 0 becomes


15 - 15 = 0 which is true.


let x = 7


3(x+2)-(3x+6)=0 becomes:


3(7+2) - (21+6) = 0 becomes:


3*9 - 27 = 0 becomes:


27 - 27 = 0 which is true.


doesn't matter what value of x you use, the equation will be true.


PROBLEM NUMBER 2


5(2z-3)=9(z+2)


simplify by removing parentheses to get:


10z - 15 = 9z + 18


subtract 9z from both sides of the equation and add 15 to both sides of the equation to get:


10z - 9z = 18 + 15


combine like terms to get:


z = 33


substitute in original equation to get:


5(2z-3)=9(z+2) becomes:


5*(2*33-3) = 9*(33+2) becomes:


5*(66-3) = 9*35 becomes


5*63 = 9*35 becomes:


315 = 315 which is true so the answer of z = 33 is good.


PROBLEM NUMBER 3


8x-(3x-1)=2


simplify by removing parentheses to get:


8x - 3x + 1 = 2


combine like terms to get:


5x + 1 = 2


subtract 1 from both sides to get:


5x = 2 - 1


combine like terms to get:


5x = 1


divide both sides by 5 to get:


x = 1/5


substitute in original equation to get:


8x-(3x-1)=2 becomes:


8*(1/5) - ((3*(1/5)) - 1) = 2


simplify by performing indicated operations to get:


8/5 - ((3/5) - 1)) = 2


simplify by removing parentheses to get:


8/5 - 3/5 + 1 = 2


simplify further to get:


5/5 + 1 = 2


simplify further to get:


1 + 1 = 2 which is true so the answer of x = 1/5 is good.