Question

If x > y and z < 0, then –xz _______ –yz.

Answer 1

$$\begin{gathered} \mathrm{If}\mathit{}x\mathit{>}y\mathrm{and}\mathit{}z\mathit{<}\mathit{0} \\ \mathrm{Now},\mathrm{multiplying}\mathrm{by}\mathit{}z,\mathrm{we}\mathrm{get} \\ \mathit{}xz\mathit{<}yz \\ \mathrm{Now},\mathrm{multiplying}\mathrm{inequality}\mathrm{by}-1 \\ \mathrm{We}\mathrm{get} \\ \mathit{-}xz\mathit{\ge }\mathit{-}yz \end{gathered}$$