Question 244891: please help me solve the equation.3(x+2)-(3x+6)=0
5(2z-3)=9(z+2),8x-(3x-1)=2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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