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Question 49859This question is from textbook Blitzer College Algebra
: Please help me understand why?
Categorizing an Equation
Q. Determine whether each question is an identity; a conditional equation, or an inconsistent equation.
Q65. 4x+5x=8x
The answer is conditional equation, but why?
Q66. 8x+2x=9x
same thing why ?????
This question is from textbook Blitzer College Algebra
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Please help me understand why?
Categorizing an Equation
Q. Determine whether each question is an identity; a conditional equation, or an inconsistent equation.
Q65. 4x+5x=8x
9X=8X.....
9X-8X=0
X=0.....IT IS AN EQUATION...WHICH IS TRUE ONLY WHEN X=0..SO YOU MAY CALL IT CONDITIONAL EQN.
The answer is conditional equation, but why?
Q66. 8x+2x=9x
same thing why ?????..SAME WAY
10X=9X
10X-9X=0
X=0...ETC...
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LET ME SHOW YOU AN IDENTITY AND INCONSISTENT EQN TO SHOW YOU THE DIFFERENCE
X+3=X+2+1...IS AN IDENTITY...SINCE IT IS TRUE FOR ANY AND EVERY VALUE OF X.
IN IDENTITIES COEFFICIENTS OF CORRESPONDING TERMS ON LHS AND RHS ARE SAME.
HERE LHS HAS 2 DIFFERENT TYPES OF TERMS..X..AND CONSTANT
SO COEFFICIENT OF X ON LHS =1= COEFFICIENT OF X ON RHS FOR IT SHOULD BE AN IDENTITY
SIMILARLY CONSTANT TERM ON LHS=3=CONSTANT TERM ON RHS=2+1=3
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X+3=X+2 IS INCONSISTENT SINCE IT CANNOT BE SATISFIED BY ANY VALUE OF X.
HERE COEFFICIENTS OF UNKNOWN WILL BE SAME ON RHS AND LHS , BUT CONSTANTS WILL DIFFER...PLEASE NOTE THAT THIS TEST IS ONLY FOR LINEAR EQNS IN ONE UNKNOWN(X) AS YOU ASKED FOR
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