Solve the Inequality for x 1+3x>=4/5x-5(x+1)

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

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

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

Simplify $\frac{4}{5} x - 5 (x + 1)$ .

Simplify each term.

Combine $\frac{4}{5}$ and $x$ .

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

Apply the distributive property.

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

Multiply $- 5$ by $1$ .

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x - 5 x \cdot 5$ .

Factor $x$ out of $4 x$ .

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

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

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

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

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

Multiply $- 5$ by $5$ .

$\frac{x (4 - 25)}{5} - 5 \leq 1 + 3 x$

Subtract $25$ from $4$ .

$\frac{x \cdot - 21}{5} - 5 \leq 1 + 3 x$

Move $- 21$ to the left of $x$ .

$\frac{- 21 \cdot x}{5} - 5 \leq 1 + 3 x$

Move the negative in front of the fraction.

$- \frac{21 x}{5} - 5 \leq 1 + 3 x$

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

Subtract $3 x$ from both sides of the inequality.

$- \frac{21 x}{5} - 5 - 3 x \leq 1$

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

$- \frac{21 x}{5} - 3 x \cdot \frac{5}{5} - 5 \leq 1$

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

$- \frac{21 x}{5} + \frac{- 3 x \cdot 5}{5} - 5 \leq 1$

Combine the numerators over the common denominator.

$\frac{- 21 x - 3 x \cdot 5}{5} - 5 \leq 1$

Simplify each term.

Simplify the numerator.

Factor $3 x$ out of $- 21 x - 3 x \cdot 5$ .

Factor $3 x$ out of $- 21 x$ .

$\frac{3 x (- 7) - 3 x \cdot 5}{5} - 5 \leq 1$

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

$\frac{3 x (- 7) + 3 x (- 1 \cdot 5)}{5} - 5 \leq 1$

Factor $3 x$ out of $3 x (- 7) + 3 x (- 1 \cdot 5)$ .

$\frac{3 x (- 7 - 1 \cdot 5)}{5} - 5 \leq 1$

Multiply $- 1$ by $5$ .

$\frac{3 x (- 7 - 5)}{5} - 5 \leq 1$

Subtract $5$ from $- 7$ .

$\frac{3 x \cdot - 12}{5} - 5 \leq 1$

Multiply $- 12$ by $3$ .

$\frac{- 36 x}{5} - 5 \leq 1$

Move the negative in front of the fraction.

$- \frac{36 x}{5} - 5 \leq 1$

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

Add $5$ to both sides of the inequality.

$- \frac{36 x}{5} \leq 1 + 5$

Add $1$ and $5$ .

$- \frac{36 x}{5} \leq 6$

Divide each term in $- \frac{36 x}{5} \leq 6$ by $- 1$ and simplify.

Divide each term in $- \frac{36 x}{5} \leq 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{36 x}{5}}{- 1} \geq \frac{6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{36 x}{5}}{1} \geq \frac{6}{- 1}$

Divide $\frac{36 x}{5}$ by $1$ .

$\frac{36 x}{5} \geq \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$\frac{36 x}{5} \geq - 6$

Multiply both sides by $5$ .

$\frac{36 x}{5} \cdot 5 \geq - 6 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{36 x}{5} \cdot 5 \geq - 6 \cdot 5$

Rewrite the expression.

$36 x \geq - 6 \cdot 5$

Simplify the right side.

Multiply $- 6$ by $5$ .

$36 x \geq - 30$

Divide each term in $36 x \geq - 30$ by $36$ and simplify.

Divide each term in $36 x \geq - 30$ by $36$ .

$\frac{36 x}{36} \geq \frac{- 30}{36}$

Simplify the left side.

Cancel the common factor of $36$ .

Cancel the common factor.

$\frac{36 x}{36} \geq \frac{- 30}{36}$

Divide $x$ by $1$ .

$x \geq \frac{- 30}{36}$

Simplify the right side.

Cancel the common factor of $- 30$ and $36$ .

Factor $6$ out of $- 30$ .

$x \geq \frac{6 (- 5)}{36}$

Cancel the common factors.

Factor $6$ out of $36$ .

$x \geq \frac{6 \cdot - 5}{6 \cdot 6}$

Cancel the common factor.

$x \geq \frac{6 \cdot - 5}{6 \cdot 6}$

Rewrite the expression.

$x \geq \frac{- 5}{6}$

Move the negative in front of the fraction.

$x \geq - \frac{5}{6}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{5}{6}$

Interval Notation:

$[- \frac{5}{6}, \infty)$

Solve the Inequality for x 1+3x>=4/5x-5(x+1)

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