Solve the Inequality for x -1/5x<=-8x-(-5x-4)-1

$- \frac{1}{5} x \leq - 8 x - (- 5 x - 4) - 1$

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

$- 8 x - (- 5 x - 4) - 1 \geq - \frac{1}{5} x$

Simplify $- 8 x - (- 5 x - 4) - 1$ .

Simplify each term.

Apply the distributive property.

$- 8 x - (- 5 x) - - 4 - 1 \geq - \frac{1}{5} x$

Multiply $- 5$ by $- 1$ .

$- 8 x + 5 x - - 4 - 1 \geq - \frac{1}{5} x$

Multiply $- 1$ by $- 4$ .

$- 8 x + 5 x + 4 - 1 \geq - \frac{1}{5} x$

Simplify by adding terms.

Add $- 8 x$ and $5 x$ .

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

Subtract $1$ from $4$ .

$- 3 x + 3 \geq - \frac{1}{5} x$

Combine $x$ and $\frac{1}{5}$ .

$- 3 x + 3 \geq - \frac{x}{5}$

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

Add $\frac{x}{5}$ to both sides of the inequality.

$- 3 x + 3 + \frac{x}{5} \geq 0$

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

$- 3 x \cdot \frac{5}{5} + \frac{x}{5} + 3 \geq 0$

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

$\frac{- 3 x \cdot 5}{5} + \frac{x}{5} + 3 \geq 0$

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 5 + x}{5} + 3 \geq 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 3 x \cdot 5 + x$ .

Factor $x$ out of $- 3 x \cdot 5$ .

$\frac{x (- 3 \cdot 5) + x}{5} + 3 \geq 0$

Raise $x$ to the power of $1$ .

$\frac{x (- 3 \cdot 5) + x^{1}}{5} + 3 \geq 0$

Factor $x$ out of $x^{1}$ .

$\frac{x (- 3 \cdot 5) + x \cdot 1}{5} + 3 \geq 0$

Factor $x$ out of $x (- 3 \cdot 5) + x \cdot 1$ .

$\frac{x (- 3 \cdot 5 + 1)}{5} + 3 \geq 0$

Multiply $- 3$ by $5$ .

$\frac{x (- 15 + 1)}{5} + 3 \geq 0$

Add $- 15$ and $1$ .

$\frac{x \cdot - 14}{5} + 3 \geq 0$

Move $- 14$ to the left of $x$ .

$\frac{- 14 \cdot x}{5} + 3 \geq 0$

Move the negative in front of the fraction.

$- \frac{14 x}{5} + 3 \geq 0$

Subtract $3$ from both sides of the inequality.

$- \frac{14 x}{5} \geq - 3$

Divide each term in $- \frac{14 x}{5} \geq - 3$ by $- 1$ and simplify.

Divide each term in $- \frac{14 x}{5} \geq - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{14 x}{5}}{- 1} \leq \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{14 x}{5}}{1} \leq \frac{- 3}{- 1}$

Divide $\frac{14 x}{5}$ by $1$ .

$\frac{14 x}{5} \leq \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$\frac{14 x}{5} \leq 3$

Multiply both sides by $5$ .

$\frac{14 x}{5} \cdot 5 \leq 3 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{14 x}{5} \cdot 5 \leq 3 \cdot 5$

Rewrite the expression.

$14 x \leq 3 \cdot 5$

Simplify the right side.

Multiply $3$ by $5$ .

$14 x \leq 15$

Divide each term in $14 x \leq 15$ by $14$ and simplify.

Divide each term in $14 x \leq 15$ by $14$ .

$\frac{14 x}{14} \leq \frac{15}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} \leq \frac{15}{14}$

Divide $x$ by $1$ .

$x \leq \frac{15}{14}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{15}{14}$

Interval Notation:

$(- \infty, \frac{15}{14}]$

Solve the Inequality for x -1/5x<=-8x-(-5x-4)-1

Related Questions

Support LCMGCF.com by disabling your adblocker.