Question

Resolva a inequação:
5(x-2) -2 (x-1) > 4 (x+2)

Answer 1

Boa tarde

5(x-2) -2(x-1) > 4(x+2)
5x-10-2x+2 > 4x+8
5x-2x-4x > 8+10-2
-x > 16
x > -16

Answer 2

Dada a inequação:

$\mathsf{5\left(x-2\right)-2\left(x-1\right)\ \textgreater \ 4\left(x+2\right)}$

Resolvendo:

$\mathsf{}\\\\\mathsf{5x-10-2\left(x-1\right)\ \textgreater \ 4\left(x+2\right)}\\\\\mathsf{5x-10-2x+2\ \textgreater \ 4\left(x+2\right)}\\\\\mathsf{5x-10-2x+2\ \textgreater \ \:4x+8}\\\\\mathsf{5x-2x-10+2\ \textgreater \ 4x+8}\\\\\mathsf{3x-8\ \textgreater \ 4x+8}\\\\\mathsf{3x-\diagup\!\!\!\!8+\diagup\!\!\!\!8\ \textgreater \ 4x+8+8}\\\\\mathsf{3x\ \textgreater \ 4x+16}\\\\\mathsf{3x-4x\ \textgreater \ \diagup\!\!\!\!\!4x-\diagup\!\!\!\!\!4x+16}\\\\\mathsf{-x\ \textgreater \ 16}\\\\\mathsf{x\ \textgreater \ -16}$

Portanto, a solução sera:

$\boxed{\mathsf{S=\left\{x\in \mathbb{R}\:,\:x\ \textgreater \ -16\right\}}}\: \: \checkmark$