Question

Resolver a inequação:(2x-3)(-x+1)≥0 *​

Answer 1

Explicação passo-a-passo:

$\sf (2x-3)\cdot(-x+1)\ge0$

• $\sf 2x-3=0$

$\sf 2x=3$

$\sf x=\dfrac{3}{2}$

• $\sf -x+1=0$

$\sf x=1$

Temos que:

$\sf~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|~~~~~~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~\dfrac{3}{2}~~~~~~~~~~~~~~~~~~~~|$

$\sf 2x-3~~~~~~~~~~~~~~~~~~~~~~~~|~~~~~~~~-~~~~~~~|~~~~~~~~~-~~~~~~~~~|~~~~~~~~+~~~~~~~|$

$\sf -x+1~~~~~~~~~~~~~~~~~~~~~~~|~~~~~~~~+~~~~~~~|~~~~~~~~~-~~~~~~~~~|~~~~~~~~-~~~~~~~|$

$\sf (2x-3)\cdot(-x+1)~~~~|~~~~~~~~-~~~~~~~|~~~~~~~~~+~~~~~~~~~|~~~~~~~~-~~~~~~~|$

Logo, $\sf 1\le x\le\dfrac{3}{2}$

$\sf S=\left\{x\in\mathbb{R}~|~1\le x\le\dfrac{3}{2}~\right\}$