Type a math problem

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Type a math problem

Solve for x

x\in (-\infty,-5]\cup [5,\infty)

$x∈(−∞,−5]∪[5,∞)$

Solution Steps

2x^2 \geq 50

$2x_{2}≥50$

Divide both sides by 2. Since 2 is >0, the inequality direction remains the same.

Divide both sides by $2$. Since $2$ is $>0$, the inequality direction remains the same.

x^{2}\geq \frac{50}{2}

$x_{2}≥250 $

Divide 50 by 2 to get 25.

Divide $50$ by $2$ to get $25$.

x^{2}\geq 25

$x_{2}≥25$

Calculate the square root of 25 and get 5. Rewrite 25 as 5^{2}\approx 25.

Calculate the square root of $25$ and get $5$. Rewrite $25$ as $5_{2}≈25$.

x^{2}\geq 5^{2}

$x_{2}≥5_{2}$

Inequality holds for |x|\geq 5.

Inequality holds for $∣x∣≥5$.

|x|\geq 5

$∣x∣≥5$

Rewrite |x|\geq 5 as x\leq -5\text{; }x\geq 5.

Rewrite $∣x∣≥5$ as $x≤−5;x≥5$.

x\leq -5\text{; }x\geq 5

$x≤−5;x≥5$

Graph

Graph Inequality

Graph Both Sides in 2D

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x^{2}\geq \frac{50}{2}

Divide both sides by 2. Since 2 is >0, the inequality direction remains the same.

x^{2}\geq 25

Divide 50 by 2 to get 25.

x^{2}\geq 5^{2}

Calculate the square root of 25 and get 5. Rewrite 25 as 5^{2}\approx 25.

|x|\geq 5

Inequality holds for |x|\geq 5.

x\leq -5\text{; }x\geq 5

Rewrite |x|\geq 5 as x\leq -5\text{; }x\geq 5.

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