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[tex]ax - b < c[/tex]
Add sides b
[tex]ax - b + b < c + b[/tex]
Simplification
[tex]ax < b + c[/tex]
Divide sides by a
[tex] \frac{a}{a} x < \frac{b + c}{a} \\ [/tex]
[tex]x < \frac{b + c}{a} \\ [/tex]
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