SOLUTION: please help me solve the equation.3(x+2)-(3x+6)=0 5(2z-3)=9(z+2),8x-(3x-1)=2

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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