Solve the Inequality for x -3<-1/5(9x+1)+x

$- 3 < - \frac{1}{5} (9 x + 1) + x$

Rewrite so $x$ is on the left side of the inequality.

$- \frac{1}{5} \cdot (9 x + 1) + x > - 3$

Simplify $- \frac{1}{5} \cdot (9 x + 1) + x$ .

Simplify each term.

Apply the distributive property.

$- \frac{1}{5} (9 x) - \frac{1}{5} \cdot 1 + x > - 3$

Multiply $- \frac{1}{5} (9 x)$ .

Multiply $9$ by $- 1$ .

$- 9 (\frac{1}{5}) x - \frac{1}{5} \cdot 1 + x > - 3$

Combine $- 9$ and $\frac{1}{5}$ .

$\frac{- 9}{5} x - \frac{1}{5} \cdot 1 + x > - 3$

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

$\frac{- 9 x}{5} - \frac{1}{5} \cdot 1 + x > - 3$

Multiply $- 1$ by $1$ .

$\frac{- 9 x}{5} - \frac{1}{5} + x > - 3$

Move the negative in front of the fraction.

$- \frac{9 x}{5} - \frac{1}{5} + x > - 3$

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

$- \frac{9 x}{5} + x \cdot \frac{5}{5} - \frac{1}{5} > - 3$

Simplify terms.

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

$- \frac{9 x}{5} + \frac{x \cdot 5}{5} - \frac{1}{5} > - 3$

Combine the numerators over the common denominator.

$\frac{- 9 x + x \cdot 5}{5} - \frac{1}{5} > - 3$

Combine the numerators over the common denominator.

$\frac{- 9 x + x \cdot 5 - 1}{5} > - 3$

Move $5$ to the left of $x$ .

$\frac{- 9 x + 5 x - 1}{5} > - 3$

Simplify terms.

Add $- 9 x$ and $5 x$ .

$\frac{- 4 x - 1}{5} > - 3$

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) - 1}{5} > - 3$

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

$\frac{- (4 x) - 1 (1)}{5} > - 3$

Factor $- 1$ out of $- (4 x) - 1 (1)$ .

$\frac{- (4 x + 1)}{5} > - 3$

Simplify the expression.

Rewrite $- (4 x + 1)$ as $- 1 (4 x + 1)$ .

$\frac{- 1 (4 x + 1)}{5} > - 3$

Move the negative in front of the fraction.

$- \frac{4 x + 1}{5} > - 3$

Divide each term in $- \frac{4 x + 1}{5} > - 3$ by $- 1$ and simplify.

Divide each term in $- \frac{4 x + 1}{5} > - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{4 x + 1}{5}}{- 1} < \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{4 x + 1}{5}}{1} < \frac{- 3}{- 1}$

Divide $\frac{4 x + 1}{5}$ by $1$ .

$\frac{4 x + 1}{5} < \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$\frac{4 x + 1}{5} < 3$

Multiply both sides by $5$ .

$\frac{4 x + 1}{5} \cdot 5 < 3 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{4 x + 1}{5} \cdot 5 < 3 \cdot 5$

Rewrite the expression.

$4 x + 1 < 3 \cdot 5$

Simplify the right side.

Multiply $3$ by $5$ .

$4 x + 1 < 15$

Solve for $x$ .

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

Subtract $1$ from both sides of the inequality.

$4 x < 15 - 1$

Subtract $1$ from $15$ .

$4 x < 14$

Divide each term in $4 x < 14$ by $4$ and simplify.

Divide each term in $4 x < 14$ by $4$ .

$\frac{4 x}{4} < \frac{14}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{14}{4}$

Divide $x$ by $1$ .

$x < \frac{14}{4}$

Simplify the right side.

Cancel the common factor of $14$ and $4$ .

Factor $2$ out of $14$ .

$x < \frac{2 (7)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x < \frac{2 \cdot 7}{2 \cdot 2}$

Cancel the common factor.

$x < \frac{2 \cdot 7}{2 \cdot 2}$

Rewrite the expression.

$x < \frac{7}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{2}$

Interval Notation:

$(- \infty, \frac{7}{2})$

Solve the Inequality for x -3<-1/5(9x+1)+x

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