Question

a) x ( x+3) - ( x-2 ) ≤ ( x-1 ) ( x+2)

Answer 1

$x\left(x+3\right)-\left(x-2\right)\le \left(x-1\right)\left(x+2\right)$
$\mathrm{Restar\:}\left(x-1\right)\left(x+2\right)\mathrm{\:de\:ambos\:lados}:$
$x\left(x+3\right)-\left(x-2\right)-\left(x-1\right)\left(x+2\right)\le \left(x-1\right)\left(x+2\right)-\left(x-1\right)\left(x+2\right)$
$\left(x+3\right)x-x-\left(x-1\right)\left(x+2\right)+2\le \:0$
$x^{2} +3x-x-x^2-x+2+2\le \:0$
$x+4\le \:0$
$\begin{bmatrix}\mathrm{Solucion:}\:&\:x\le \:-4\:\\ \:\mathrm{Notacion\:intervalo}&\:(-\infty \:,\:-4]\end{bmatrix}$