From Wikipedia's definition of algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

$4.5$ in $x - 4.5$ is not an integer, so it would be algebraic or not?


$$X - \frac{9}{2} = \frac{2X - 9}{2}$$

so according to the definition, your expression is indeed an algebraic expression.

  • $\begingroup$ Its more precise to be rational algebraic expression $\endgroup$ – user629353 Dec 27 '18 at 13:33
  • $\begingroup$ But what if when 4.5 is replaced by π, then still algebraic expression or not? $\endgroup$ – user629353 Dec 27 '18 at 13:37
  • $\begingroup$ @user629353 then it certainly is not. Can you see why? $\endgroup$ – Edward Evans Dec 27 '18 at 13:37
  • 1
    $\begingroup$ Because pi is irrational? $\endgroup$ – user629353 Dec 27 '18 at 13:47

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