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Linear inequalities with one variable

What counts as a linear inequality
A linear inequality in one variable is usually brought to one of the forms: ax>b,ax<b,axb,axb,ax>b,\quad ax<b,\quad ax\geq b,\quad ax\leq b, with a0a\neq 0. (Strict and non-strict can be mixed.) Then divide by aa and watch the sign: if a>0a>0, the inequality sign stays; if a<0a<0 — it flips, as in the previous lesson. Special cases: after simplification you may get a contradiction like 0>50>5 or an identity like x>x3x>x-3 ("0>30>-3, always true") — then the solution set is empty or the whole line; the interactive below shows typical "nice" cases with one ray or segment on the axis.
Moving terms between sides — like an equation, the inequality sign does not change
Dividing the whole inequality by negative aa — flip the sign
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