Toolkit 105Inequality Properties and TransformationsBasic Properties of Inequalitiesa,b,c∈Ra,b,c\in\mathbb{R}a,b,c∈Ra<b⟹a+c<b+ca<b\Longrightarrow a+c<b+ca<b⟹a+c<b+ca<b⟹a−c<b−ca<b\Longrightarrow a-c<b-ca<b⟹a−c<b−cc>0, a<b⟹ac<bcc>0,\ a<b\Longrightarrow ac<bcc>0, a<b⟹ac<bcc<0, a<b⟹ac>bcc<0,\ a<b\Longrightarrow ac>bcc<0, a<b⟹ac>bcPowers of Inequalitiesn∈Z+∪{0}, a<b⟹a2n+1<b2n+1n\in\mathbb{Z}^+\cup\{0\},\ a<b\Longrightarrow a^{2n+1}<b^{2n+1}n∈Z+∪{0}, a<b⟹a2n+1<b2n+1