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4211222102x122≥7 x16x^2≥9

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Type your math problem... 4211222102x122≥7 x16x^2≥9

Question

Solve the inequality

$Solve for x$

solver-selected-icon

\frac{3 1764}{28} \leq x \leq \frac{899095918777}{14}

Alternative Form

x \in [\frac{3 1764}{28}, \frac{899095918777}{14}]

Evaluate

4211222102 x 122 \geq 7 x 16 x^{2} \geq 9

Separate into two inequalities

{4211222102 x \times 122 \geq 7 x \times 16 x^{2} 7 x \times 16 x^{2} \geq 9

Solve the inequality

More Steps

Evaluate

4211222102 x \times 122 \geq 7 x \times 16 x^{2}

Multiply the terms

513769096444 x \geq 7 x \times 16 x^{2}

Multiply

More Steps

513769096444 x \geq 112 x^{3}

Add or subtract both sides

513769096444 x - 112 x^{3} \geq 0

Factor the expression

4 x (128442274111 - 28 x^{2}) \geq 0

Divide both sides

x (128442274111 - 28 x^{2}) \geq 0

Separate the inequality into 2 possible cases

{x \geq 0 128442274111 - 28 x^{2} \geq 0 {x \leq 0 128442274111 - 28 x^{2} \leq 0

Solve the inequality

More Steps

{x \geq 0 - \frac{899095918777}{14} \leq x \leq \frac{899095918777}{14} {x \leq 0 128442274111 - 28 x^{2} \leq 0

Solve the inequality

More Steps

{x \geq 0 - \frac{899095918777}{14} \leq x \leq \frac{899095918777}{14} {x \leq 0 x \in (- \infty, - \frac{899095918777}{14}] \cup [\frac{899095918777}{14}, + \infty)

Find the intersection

0 \leq x \leq \frac{899095918777}{14} {x \leq 0 x \in (- \infty, - \frac{899095918777}{14}] \cup [\frac{899095918777}{14}, + \infty)

Find the intersection

0 \leq x \leq \frac{899095918777}{14} x \leq - \frac{899095918777}{14}

Find the union

x \in (- \infty, - \frac{899095918777}{14}] \cup [0, \frac{899095918777}{14}]

{x \in (- \infty, - \frac{899095918777}{14}] \cup [0, \frac{899095918777}{14}] 7 x \times 16 x^{2} \geq 9

Solve the inequality

More Steps

{x \in (- \infty, - \frac{899095918777}{14}] \cup [0, \frac{899095918777}{14}] x \geq \frac{3 1764}{28}

Solution

\frac{3 1764}{28} \leq x \leq \frac{899095918777}{14}

Alternative Form

x \in [\frac{3 1764}{28}, \frac{899095918777}{14}]

Show Solution