Solve the Inequality for x -5-(x+4)/5>11-3x

$- 5 - \frac{x + 4}{5} > 11 - 3 x$

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

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

$- 5 \cdot \frac{5}{5} - \frac{x + 4}{5} > 11 - 3 x$

Simplify terms.

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

$\frac{- 5 \cdot 5}{5} - \frac{x + 4}{5} > 11 - 3 x$

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 5 - (x + 4)}{5} > 11 - 3 x$

Simplify the numerator.

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

Reorder $- 5 \cdot 5$ and $- (x + 4)$ .

$\frac{- (x + 4) - 5 \cdot 5}{5} > 11 - 3 x$

Factor $- 1$ out of $- 5 \cdot 5$ .

$\frac{- (x + 4) - (5 \cdot 5)}{5} > 11 - 3 x$

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

$\frac{- (x + 4 + 5 \cdot 5)}{5} > 11 - 3 x$

Multiply $5$ by $5$ .

$\frac{- (x + 4 + 25)}{5} > 11 - 3 x$

Add $4$ and $25$ .

$\frac{- (x + 29)}{5} > 11 - 3 x$

Move the negative in front of the fraction.

$- \frac{x + 29}{5} > 11 - 3 x$

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

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

$- \frac{x + 29}{5} + 3 x > 11$

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

$- \frac{x + 29}{5} + 3 x \cdot \frac{5}{5} > 11$

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

$- \frac{x + 29}{5} + \frac{3 x \cdot 5}{5} > 11$

Combine the numerators over the common denominator.

$\frac{- (x + 29) + 3 x \cdot 5}{5} > 11$

Simplify the numerator.

Apply the distributive property.

$\frac{- x - 1 \cdot 29 + 3 x \cdot 5}{5} > 11$

Multiply $- 1$ by $29$ .

$\frac{- x - 29 + 3 x \cdot 5}{5} > 11$

Multiply $5$ by $3$ .

$\frac{- x - 29 + 15 x}{5} > 11$

Add $- x$ and $15 x$ .

$\frac{14 x - 29}{5} > 11$

Multiply both sides by $5$ .

$\frac{14 x - 29}{5} \cdot 5 > 11 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{14 x - 29}{5} \cdot 5 > 11 \cdot 5$

Rewrite the expression.

$14 x - 29 > 11 \cdot 5$

Simplify the right side.

Multiply $11$ by $5$ .

$14 x - 29 > 55$

Solve for $x$ .

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

Add $29$ to both sides of the inequality.

$14 x > 55 + 29$

Add $55$ and $29$ .

$14 x > 84$

Divide each term in $14 x > 84$ by $14$ and simplify.

Divide each term in $14 x > 84$ by $14$ .

$\frac{14 x}{14} > \frac{84}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} > \frac{84}{14}$

Divide $x$ by $1$ .

$x > \frac{84}{14}$

Simplify the right side.

Divide $84$ by $14$ .

$x > 6$

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$

Solve the Inequality for x -5-(x+4)/5>11-3x

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