Question

Determine conjunto solução da inequação, considerando U=Q

Answer 1

$\boxed{\begin{array}{l}\sf-\dfrac{1}{3}\cdot\bigg(\dfrac{3}{2}-2x\bigg)>\dfrac{1}{2}\\\underline{\rm multiplicando~por~6~a~inequac_{\!\!,}\tilde ao~temos:}\\\sf 6\cdot-\dfrac{1}{3}\cdot\bigg(\dfrac{3}{2}-3x\bigg)>\dfrac{1}{2}\cdot6\\\sf -2\cdot\bigg(\dfrac{3}{2}-2x\bigg)>3\\\sf-3+4x>3\\\sf 4x>3+3\\\sf 4x>6\\\sf x>\dfrac{6\div2}{4\div2}\\\sf x>\dfrac{3}{2}\\\sf S=\bigg\{x\in\mathbb{Q}/x>\dfrac{3}{2}\bigg\}\end{array}}$