Question

(x + 3)(x - 1) ≤ x(x + 5)

Answer 1

Resposta:

Explicação passo a passo:

$(x+3).(x-1)\leq x.(x+5)$

$x^{2} -x+3x-3\leq x^{2} +5x$

$Cancela\:x^{2} \:dos\;dois\:lados...$

    $-x+3x-5x\leq 3$

             $-3x\leq 3$

                $3x\geq -3$

                  $x\geq -\frac{3}{3}$

                  $x\geq -1$

Answer 2

$\displaystyle \sf (x+3)(x-1)\leq x(x+5) \\\\ x^2-2x-3 \leq x^2+5x \\\\ x^2-2x-3-x^2-5x \leq 0 \\\\ -7x-3 \leq 0 \\\\ Ra{\'i}}z :-7x-3 = 0 \\\\\ x = \frac{-3}{7}$

$\displaystyle \sf -7x-3 \leq 0 \to \text{fun\c c\~ao decrescente } \\\\ \text{antes da raiz positiva e depois negativa. \ } Portanto : \\\\ \huge\boxed{\sf S = \left\{x\in\mathbb{R} \ | \ x \geq \frac{-3}{7}\right\} }\checkmark$