Solve for x -2/5x-9<9/10

$- \frac{2}{5} x - 9 < \frac{9}{10}$

Step 1

Simplify each term.

Combine $x$ and $\frac{2}{5}$ .

$- \frac{x \cdot 2}{5} - 9 < \frac{9}{10}$

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

$- \frac{2 x}{5} - 9 < \frac{9}{10}$

Step 2

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

Add $9$ to both sides of the inequality.

$- \frac{2 x}{5} < \frac{9}{10} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{2 x}{5} < \frac{9}{10} + 9 \cdot \frac{10}{10}$

Combine $9$ and $\frac{10}{10}$ .

$- \frac{2 x}{5} < \frac{9}{10} + \frac{9 \cdot 10}{10}$

Combine the numerators over the common denominator.

$- \frac{2 x}{5} < \frac{9 + 9 \cdot 10}{10}$

Simplify the numerator.

Multiply $9$ by $10$ .

$- \frac{2 x}{5} < \frac{9 + 90}{10}$

Add $9$ and $90$ .

$- \frac{2 x}{5} < \frac{99}{10}$

Step 3

Divide each term in $- \frac{2 x}{5} < \frac{99}{10}$ by $- 1$ and simplify.

Divide each term in $- \frac{2 x}{5} < \frac{99}{10}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 x}{5}}{- 1} > \frac{\frac{99}{10}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{5}}{1} > \frac{\frac{99}{10}}{- 1}$

Divide $\frac{2 x}{5}$ by $1$ .

$\frac{2 x}{5} > \frac{\frac{99}{10}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{99}{10}}{- 1}$ .

$\frac{2 x}{5} > - 1 \cdot \frac{99}{10}$

Rewrite $- 1 \cdot \frac{99}{10}$ as $- \frac{99}{10}$ .

$\frac{2 x}{5} > - \frac{99}{10}$

Step 4

Multiply both sides by $5$ .

$\frac{2 x}{5} \cdot 5 > - \frac{99}{10} \cdot 5$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 > - \frac{99}{10} \cdot 5$

Rewrite the expression.

$2 x > - \frac{99}{10} \cdot 5$

Simplify the right side.

Simplify $- \frac{99}{10} \cdot 5$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{99}{10}$ into the numerator.

$2 x > \frac{- 99}{10} \cdot 5$

Factor $5$ out of $10$ .

$2 x > \frac{- 99}{5 (2)} \cdot 5$

Cancel the common factor.

$2 x > \frac{- 99}{5 \cdot 2} \cdot 5$

Rewrite the expression.

$2 x > \frac{- 99}{2}$

Move the negative in front of the fraction.

$2 x > - \frac{99}{2}$

Step 6

Divide each term in $2 x > - \frac{99}{2}$ by $2$ and simplify.

Divide each term in $2 x > - \frac{99}{2}$ by $2$ .

$\frac{2 x}{2} > \frac{- \frac{99}{2}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- \frac{99}{2}}{2}$

Divide $x$ by $1$ .

$x > \frac{- \frac{99}{2}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{99}{2} \cdot \frac{1}{2}$

Multiply $- \frac{99}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{99}{2}$ .

$x > - \frac{99}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x > - \frac{99}{4}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{99}{4}$

Interval Notation:

$(- \frac{99}{4}, \infty)$

Solve for x -2/5x-9<9/10

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