Solve the Inequality for x x/5-x/4<=9/10

$\frac{x}{5} - \frac{x}{4} \leq \frac{9}{10}$

Simplify $\frac{x}{5} - \frac{x}{4}$ .

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{5} \cdot \frac{4}{4} - \frac{x}{4} \leq \frac{9}{10}$

To write $- \frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{5}{5} \leq \frac{9}{10}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{5}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{5 \cdot 4} - \frac{x}{4} \cdot \frac{5}{5} \leq \frac{9}{10}$

Multiply $5$ by $4$ .

$\frac{x \cdot 4}{20} - \frac{x}{4} \cdot \frac{5}{5} \leq \frac{9}{10}$

Multiply $\frac{x}{4}$ by $\frac{5}{5}$ .

$\frac{x \cdot 4}{20} - \frac{x \cdot 5}{4 \cdot 5} \leq \frac{9}{10}$

Multiply $4$ by $5$ .

$\frac{x \cdot 4}{20} - \frac{x \cdot 5}{20} \leq \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 5}{20} \leq \frac{9}{10}$

Simplify the numerator.

Factor $x$ out of $x \cdot 4 - x \cdot 5$ .

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4) - x \cdot 5}{20} \leq \frac{9}{10}$

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (4) + x (- 1 \cdot 5)}{20} \leq \frac{9}{10}$

Factor $x$ out of $x (4) + x (- 1 \cdot 5)$ .

$\frac{x (4 - 1 \cdot 5)}{20} \leq \frac{9}{10}$

Multiply $- 1$ by $5$ .

$\frac{x (4 - 5)}{20} \leq \frac{9}{10}$

Subtract $5$ from $4$ .

$\frac{x \cdot - 1}{20} \leq \frac{9}{10}$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{20} \leq \frac{9}{10}$

Move the negative in front of the fraction.

$- \frac{x}{20} \leq \frac{9}{10}$

Divide each term in $- \frac{x}{20} \leq \frac{9}{10}$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{20} \leq \frac{9}{10}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{20}}{- 1} \geq \frac{\frac{9}{10}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{20}}{1} \geq \frac{\frac{9}{10}}{- 1}$

Divide $\frac{x}{20}$ by $1$ .

$\frac{x}{20} \geq \frac{\frac{9}{10}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{9}{10}}{- 1}$ .

$\frac{x}{20} \geq - 1 \cdot \frac{9}{10}$

Rewrite $- 1 \cdot \frac{9}{10}$ as $- \frac{9}{10}$ .

$\frac{x}{20} \geq - \frac{9}{10}$

Multiply both sides by $20$ .

$\frac{x}{20} \cdot 20 \geq - \frac{9}{10} \cdot 20$

Simplify.

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{x}{20} \cdot 20 \geq - \frac{9}{10} \cdot 20$

Rewrite the expression.

$x \geq - \frac{9}{10} \cdot 20$

Simplify the right side.

Simplify $- \frac{9}{10} \cdot 20$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{9}{10}$ into the numerator.

$x \geq \frac{- 9}{10} \cdot 20$

Factor $10$ out of $20$ .

$x \geq \frac{- 9}{10} \cdot (10 (2))$

Cancel the common factor.

$x \geq \frac{- 9}{10} \cdot (10 \cdot 2)$

Rewrite the expression.

$x \geq - 9 \cdot 2$

Multiply $- 9$ by $2$ .

$x \geq - 18$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 18$

Interval Notation:

$[- 18, \infty)$

Solve the Inequality for x x/5-x/4<=9/10

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