What counts as a linear inequality
A linear inequality in one variable is usually brought to one of the forms:
ax>b,ax<b,ax≥b,ax≤b, with a=0. (Strict and non-strict can be mixed.)
Then divide by a and watch the sign: if a>0, the inequality sign stays; if a<0 — it flips, as in the previous lesson.
Special cases: after simplification you may get a contradiction like 0>5 or an identity like x>x−3 ("0>−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 a — flip the sign
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