Algebra Examples

$- \frac{50 x}{3} - \frac{11}{6} \geq \frac{163}{2}$

Step 1

Move all terms not containing $x$ to the right side of the inequality.

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Add $\frac{11}{6}$ to both sides of the inequality.

$- \frac{50 x}{3} \geq \frac{163}{2} + \frac{11}{6}$

To write $\frac{163}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{50 x}{3} \geq \frac{163}{2} \cdot \frac{3}{3} + \frac{11}{6}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{163}{2}$ by $\frac{3}{3}$ .

$- \frac{50 x}{3} \geq \frac{163 \cdot 3}{2 \cdot 3} + \frac{11}{6}$

Multiply $2$ by $3$ .

$- \frac{50 x}{3} \geq \frac{163 \cdot 3}{6} + \frac{11}{6}$

Combine the numerators over the common denominator.

$- \frac{50 x}{3} \geq \frac{163 \cdot 3 + 11}{6}$

Simplify the numerator.

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Multiply $163$ by $3$ .

$- \frac{50 x}{3} \geq \frac{489 + 11}{6}$

Add $489$ and $11$ .

$- \frac{50 x}{3} \geq \frac{500}{6}$

Cancel the common factor of $500$ and $6$ .

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Factor $2$ out of $500$ .

$- \frac{50 x}{3} \geq \frac{2 (250)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$- \frac{50 x}{3} \geq \frac{2 \cdot 250}{2 \cdot 3}$

Cancel the common factor.

$- \frac{50 x}{3} \geq \frac{2 \cdot 250}{2 \cdot 3}$

Rewrite the expression.

$- \frac{50 x}{3} \geq \frac{250}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 50 x \geq 250$

Step 3

Divide each term in $- 50 x \geq 250$ by $- 50$ and simplify.

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Divide each term in $- 50 x \geq 250$ by $- 50$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 50 x}{- 50} \leq \frac{250}{- 50}$

Simplify the left side.

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Cancel the common factor of $- 50$ .

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Cancel the common factor.

$\frac{- 50 x}{- 50} \leq \frac{250}{- 50}$

Divide $x$ by $1$ .

$x \leq \frac{250}{- 50}$

Simplify the right side.

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Divide $250$ by $- 50$ .

$x \leq - 5$

Step 4