Solve the Inequality for x 2+3/5(-9x-3)>-3x-5/2

$2 + \frac{3}{5} (- 9 x - 3) > - 3 x - \frac{5}{2}$

Simplify $2 + \frac{3}{5} \cdot (- 9 x - 3)$ .

Simplify each term.

Apply the distributive property.

$2 + \frac{3}{5} (- 9 x) + \frac{3}{5} \cdot - 3 > - 3 x - \frac{5}{2}$

Multiply $\frac{3}{5} (- 9 x)$ .

Combine $- 9$ and $\frac{3}{5}$ .

$2 + \frac{- 9 \cdot 3}{5} x + \frac{3}{5} \cdot - 3 > - 3 x - \frac{5}{2}$

Multiply $- 9$ by $3$ .

$2 + \frac{- 27}{5} x + \frac{3}{5} \cdot - 3 > - 3 x - \frac{5}{2}$

Combine $\frac{- 27}{5}$ and $x$ .

$2 + \frac{- 27 x}{5} + \frac{3}{5} \cdot - 3 > - 3 x - \frac{5}{2}$

Multiply $\frac{3}{5} \cdot - 3$ .

Combine $\frac{3}{5}$ and $- 3$ .

$2 + \frac{- 27 x}{5} + \frac{3 \cdot - 3}{5} > - 3 x - \frac{5}{2}$

Multiply $3$ by $- 3$ .

$2 + \frac{- 27 x}{5} + \frac{- 9}{5} > - 3 x - \frac{5}{2}$

Simplify each term.

Move the negative in front of the fraction.

$2 - \frac{(27) x}{5} + \frac{- 9}{5} > - 3 x - \frac{5}{2}$

Move the negative in front of the fraction.

$2 - \frac{27 x}{5} - \frac{9}{5} > - 3 x - \frac{5}{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{27 x}{5} + 2 \cdot \frac{5}{5} - \frac{9}{5} > - 3 x - \frac{5}{2}$

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

$- \frac{27 x}{5} + \frac{2 \cdot 5}{5} - \frac{9}{5} > - 3 x - \frac{5}{2}$

Combine the numerators over the common denominator.

$- \frac{27 x}{5} + \frac{2 \cdot 5 - 9}{5} > - 3 x - \frac{5}{2}$

Simplify the numerator.

Multiply $2$ by $5$ .

$- \frac{27 x}{5} + \frac{10 - 9}{5} > - 3 x - \frac{5}{2}$

Subtract $9$ from $10$ .

$- \frac{27 x}{5} + \frac{1}{5} > - 3 x - \frac{5}{2}$

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

Add $3 x$ to both sides of the inequality.

$- \frac{27 x}{5} + \frac{1}{5} + 3 x > - \frac{5}{2}$

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{27 x}{5} + 3 x \cdot \frac{5}{5} + \frac{1}{5} > - \frac{5}{2}$

Combine $3 x$ and $\frac{5}{5}$ .

$- \frac{27 x}{5} + \frac{3 x \cdot 5}{5} + \frac{1}{5} > - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{- 27 x + 3 x \cdot 5}{5} + \frac{1}{5} > - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{- 27 x + 3 x \cdot 5 + 1}{5} > - \frac{5}{2}$

Multiply $5$ by $3$ .

$\frac{- 27 x + 15 x + 1}{5} > - \frac{5}{2}$

Add $- 27 x$ and $15 x$ .

$\frac{- 12 x + 1}{5} > - \frac{5}{2}$

Factor $- 1$ out of $- 12 x$ .

$\frac{- (12 x) + 1}{5} > - \frac{5}{2}$

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- (12 x) - 1 (- 1)}{5} > - \frac{5}{2}$

Factor $- 1$ out of $- (12 x) - 1 (- 1)$ .

$\frac{- (12 x - 1)}{5} > - \frac{5}{2}$

Rewrite $- (12 x - 1)$ as $- 1 (12 x - 1)$ .

$\frac{- 1 (12 x - 1)}{5} > - \frac{5}{2}$

Move the negative in front of the fraction.

$- \frac{12 x - 1}{5} > - \frac{5}{2}$

Divide each term in $- \frac{12 x - 1}{5} > - \frac{5}{2}$ by $- 1$ and simplify.

Divide each term in $- \frac{12 x - 1}{5} > - \frac{5}{2}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{12 x - 1}{5}}{- 1} < \frac{- \frac{5}{2}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{12 x - 1}{5}}{1} < \frac{- \frac{5}{2}}{- 1}$

Divide $\frac{12 x - 1}{5}$ by $1$ .

$\frac{12 x - 1}{5} < \frac{- \frac{5}{2}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$\frac{12 x - 1}{5} < \frac{\frac{5}{2}}{1}$

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

$\frac{12 x - 1}{5} < \frac{5}{2}$

Multiply both sides by $5$ .

$\frac{12 x - 1}{5} \cdot 5 < \frac{5}{2} \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{12 x - 1}{5} \cdot 5 < \frac{5}{2} \cdot 5$

Rewrite the expression.

$12 x - 1 < \frac{5}{2} \cdot 5$

Simplify the right side.

Multiply $\frac{5}{2} \cdot 5$ .

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

$12 x - 1 < \frac{5 \cdot 5}{2}$

Multiply $5$ by $5$ .

$12 x - 1 < \frac{25}{2}$

Solve for $x$ .

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

Add $1$ to both sides of the inequality.

$12 x < \frac{25}{2} + 1$

Write $1$ as a fraction with a common denominator.

$12 x < \frac{25}{2} + \frac{2}{2}$

Combine the numerators over the common denominator.

$12 x < \frac{25 + 2}{2}$

Add $25$ and $2$ .

$12 x < \frac{27}{2}$

Divide each term in $12 x < \frac{27}{2}$ by $12$ and simplify.

Divide each term in $12 x < \frac{27}{2}$ by $12$ .

$\frac{12 x}{12} < \frac{\frac{27}{2}}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} < \frac{\frac{27}{2}}{12}$

Divide $x$ by $1$ .

$x < \frac{\frac{27}{2}}{12}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{27}{2} \cdot \frac{1}{12}$

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$x < \frac{3 (9)}{2} \cdot \frac{1}{12}$

Factor $3$ out of $12$ .

$x < \frac{3 \cdot 9}{2} \cdot \frac{1}{3 \cdot 4}$

Cancel the common factor.

$x < \frac{3 \cdot 9}{2} \cdot \frac{1}{3 \cdot 4}$

Rewrite the expression.

$x < \frac{9}{2} \cdot \frac{1}{4}$

Multiply $\frac{9}{2}$ by $\frac{1}{4}$ .

$x < \frac{9}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x < \frac{9}{8}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{9}{8}$

Interval Notation:

$(- \infty, \frac{9}{8})$

Solve the Inequality for x 2+3/5(-9x-3)>-3x-5/2

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