Answer to Question #22693 in Algebra for Kristen Woods

Question

Solve the given equation and determine whether the equation is an identity, a conditional equation or an inconsistent equation.

1a. 2(x+5)=4x-2(x-5)

1b. (x/2)-(3/4)=(10-15x)/6

Answer 1

1a. 2(x+5)=4x-2(x-5)
2x+10=4x-2x+10
2x+10=2x+10
0=0
so all x satisfy this equation then it is an identity
1b.(x/2)-(3/4)=(10-15x)/6x/2 -3/4=10/6-(15/6) x
x/2-3/4=5/3-(3/2)x
x/2+(3/2) x=5/3+3/4
2x=20/12+9/12
2x=29/12
x=29/24
equation is conditional