# Solve for: 5x^2+7x >= 0

## Expression: $5{x}^{2}+7x \geq 0$

Factor out $x$ from the expression

$x \times \left( 5x+7 \right) \geq 0$

Separate the inequality into two possible cases

$\begin{array} { l }\left\{\begin{array} { l } x \geq 0 \\ 5x+7 \geq 0\end{array} \right.,\\\left\{\begin{array} { l } x \leq 0 \\ 5x+7 \leq 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \geq 0 \\ x \geq -\frac{ 7 }{ 5 }\end{array} \right.,\\\left\{\begin{array} { l } x \leq 0 \\ 5x+7 \leq 0\end{array} \right.\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\left\{\begin{array} { l } x \geq 0 \\ x \geq -\frac{ 7 }{ 5 }\end{array} \right.,\\\left\{\begin{array} { l } x \leq 0 \\ x \leq -\frac{ 7 }{ 5 }\end{array} \right.\end{array}$

Find the intersection

$\begin{array} { l }x \in \left[ 0, +\infty\right\rangle,\\\left\{\begin{array} { l } x \leq 0 \\ x \leq -\frac{ 7 }{ 5 }\end{array} \right.\end{array}$

Find the intersection

$\begin{array} { l }x \in \left[ 0, +\infty\right\rangle,\\x \in \left\langle-\infty, -\frac{ 7 }{ 5 }\right]\end{array}$

Find the union

$x \in \left\langle-\infty, -\frac{ 7 }{ 5 }\right] \cup \left[ 0, +\infty\right\rangle$

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