Question

$2x^{2}+5x-3\geq0$

Answer 1

Respuesta:

x∈ $\left[\begin{array}{ccc}-\infty \,,-3}\end{array}\right]$

Explicación paso a paso:

-Reescribes la expresión:

$2x^{2}+6x-x\geq0$

-Factorizar:

$2x(x+3)-(x+3)\geq0$

$(x+3)(2x-1)\geq0$

$\left \{ {{x+3\geq0 } \atop {{2x-1\geq0}} \right.$

$\left \{ {{x+3\leq0} \atop {{2x-1\leq0}} \right.$

$\left \{ {{x\geq-3} \atop {x\geq\frac{1}{2} }} \right.$

$\left \{ {{x\leq-3} \atop {x\leq\frac{1}{2} }} \right.$

x∈ $\left[\begin{array}{ccc}\frac{1}{2} \,, \infty+}\end{array}\right]$

x∈ $\left[\begin{array}{ccc}-\infty \,,-3}\end{array}\right]$