Equations and inequalities with a parameter

Parameter as a “fixed letter”

In an equation of the form $f(x,a)=0$ you work with $x$ as in ordinary algebra, but intermediate formulas depend on $a$ . The answer is written by cases: for example “if $a=0$ — linear; if $a\neq0$ — divide by $a$ ”. For inequalities you also watch the sign of the factor $a$ when dividing.

Check each case separately for consistency (especially for quadratics and $D$ )

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