Evaluate x/5>=1-x/10

$\frac{x}{5} \geq 1 - \frac{x}{10}$

Multiply both sides of the equation by $5$ .

$x \geq 1 \cdot (5) - \frac{x}{10} \cdot 5$

Simplify each term.

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Multiply $5$ by $1$ .

$x \geq 5 - \frac{x}{10} \cdot 5$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{x}{10}$ into the numerator.

$x \geq 5 + \frac{- x}{10} \cdot 5$

Factor $5$ out of $10$ .

$x \geq 5 + \frac{- x}{5 (2)} \cdot 5$

Cancel the common factor.

$x \geq 5 + \frac{- x}{5 \cdot 2} \cdot 5$

Rewrite the expression.

$x \geq 5 + \frac{- x}{2}$

Move the negative in front of the fraction.

$x \geq 5 - \frac{x}{2}$

Move all terms containing $x$ to the left side of the inequality.

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Add $\frac{x}{2}$ to both sides of the inequality.

$x + \frac{x}{2} \geq 5$

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x \cdot \frac{2}{2} + \frac{x}{2} \geq 5$

Combine $x$ and $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{x}{2} \geq 5$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} \geq 5$

Simplify the numerator.

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Move $2$ to the left of $x$ .

$\frac{2 \cdot x + x}{2} \geq 5$

Add $2 x$ and $x$ .

$\frac{3 x}{2} \geq 5$

Multiply both sides of the equation by $2$ .

$3 x \geq 5 \cdot (2)$

Multiply $5$ by $2$ .

$3 x \geq 10$

Divide each term by $3$ and simplify.

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Divide each term in $3 x \geq 10$ by $3$ .

$\frac{3 x}{3} \geq \frac{10}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 x}{3} \geq \frac{10}{3}$

Divide $x$ by $1$ .

$x \geq \frac{10}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{10}{3}$

Interval Notation:

$[\frac{10}{3}, \infty)$

Evaluate x/5>=1-x/10

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