Question

Resolver em R: (2x – 1) ⋅ (x – 1) ⋅ (x + 3 ) ≥ 0.

Answer 1

Explicação passo-a-passo:

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

$\bullet~2x-1=0~2x=1~\longrightarrow~x=\dfrac{1}{2}$

$x-1=0~\longrightarrow~x=1$

$x+3=0~\longrightarrow~x=-3$

$.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-3~~~~~~~~~~~~~~~\dfrac{1}{2}~~~~~~~~~~~~~~1$

$~~~~~~~~~2x-1~~~~~~~~~~~~~~~~~~~~~~~~~-~~~~~~|~~~~~~-~~~~~|~~~~~~+~~~~~~|~~~~+$

$~~~~~~~~~~x-1~~~~~~~~~~~~~~~~~~~~~~~~~~-~~~~~~|~~~~~-~~~~~~|~~~~~~-~~~~~~|~~~~~+$

$~~~~~~~~~x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~-~~~~~~|~~~~~~+~~~~~|~~~~~~+~~~~~~|~~~~~+$

$(2x-1)(x-1)(x+3)~~~~~~~-~~~~~|~~~~~~+~~~~~~|~~~~~~~-~~~~|~~~~~+$

Logo, $S=\{x\in\mathbb{R}~|~-3\le x\le\frac{1}{2}~\text{ou}~x\ge1 \}$