# work out the value of a - b from the identity $ax+18=2(x-b)$

How do I solve the following question?

You are given the algebraic identity:
$ax+18=2(x-b)$

Work out the values of $a-b$

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$2 - \dfrac{18}{-2} = ?$ –  njguliyev Oct 20 '13 at 15:20
11 .but how did you get it? Explain please –  user100315 Oct 20 '13 at 15:27
"Algebraic identity" means that it is true for all values of $x$, i.e. the coefficients of the powers of $x$ must be equal. –  njguliyev Oct 20 '13 at 15:31

The given equality can be written as follows:

$ax+18=2(x-b)$
or, $ax+18=2x-2b$
or, $(a-2)x+(18+2b)=0$

Science this is an identity in $x$ ,it follows that

$a-2=0 , 18+2b=0$

Thus $a=2$ and $b=-9$
Hence, $a-b=2-(-9)=11$

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