Question #22693

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

Expert's answer

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

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

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