Solve the Inequality for x -9x+2<=-3(-4/5x-10)-1/5x

$- 9 x + 2 \leq - 3 (- \frac{4}{5} x - 10) - \frac{1}{5} x$

Step 1

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

$- 3 (- \frac{4}{5} x - 10) - \frac{1}{5} x \geq - 9 x + 2$

Step 2

Simplify $- 3 (- \frac{4}{5} x - 10) - \frac{1}{5} x$ .

Simplify each term.

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

$- 3 (- \frac{x \cdot 4}{5} - 10) - \frac{1}{5} x \geq - 9 x + 2$

Move $4$ to the left of $x$ .

$- 3 (- \frac{4 x}{5} - 10) - \frac{1}{5} x \geq - 9 x + 2$

Apply the distributive property.

$- 3 (- \frac{4 x}{5}) - 3 \cdot - 10 - \frac{1}{5} x \geq - 9 x + 2$

Multiply $- 3 (- \frac{4 x}{5})$ .

Multiply $- 1$ by $- 3$ .

$3 \frac{4 x}{5} - 3 \cdot - 10 - \frac{1}{5} x \geq - 9 x + 2$

Combine $3$ and $\frac{4 x}{5}$ .

$\frac{3 (4 x)}{5} - 3 \cdot - 10 - \frac{1}{5} x \geq - 9 x + 2$

Multiply $4$ by $3$ .

$\frac{12 x}{5} - 3 \cdot - 10 - \frac{1}{5} x \geq - 9 x + 2$

Multiply $- 3$ by $- 10$ .

$\frac{12 x}{5} + 30 - \frac{1}{5} x \geq - 9 x + 2$

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

$\frac{12 x}{5} + 30 - \frac{x}{5} \geq - 9 x + 2$

Simplify terms.

Combine the numerators over the common denominator.

$30 + \frac{12 x - x}{5} \geq - 9 x + 2$

Subtract $x$ from $12 x$ .

$30 + \frac{11 x}{5} \geq - 9 x + 2$

Step 3

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

Add $9 x$ to both sides of the inequality.

$30 + \frac{11 x}{5} + 9 x \geq 2$

To write $9 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$30 + \frac{11 x}{5} + 9 x \cdot \frac{5}{5} \geq 2$

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

$30 + \frac{11 x}{5} + \frac{9 x \cdot 5}{5} \geq 2$

Combine the numerators over the common denominator.

$30 + \frac{11 x + 9 x \cdot 5}{5} \geq 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $11 x + 9 x \cdot 5$ .

Factor $x$ out of $11 x$ .

$30 + \frac{x \cdot 11 + 9 x \cdot 5}{5} \geq 2$

Factor $x$ out of $9 x \cdot 5$ .

$30 + \frac{x \cdot 11 + x (9 \cdot 5)}{5} \geq 2$

Factor $x$ out of $x \cdot 11 + x (9 \cdot 5)$ .

$30 + \frac{x (11 + 9 \cdot 5)}{5} \geq 2$

Multiply $9$ by $5$ .

$30 + \frac{x (11 + 45)}{5} \geq 2$

Add $11$ and $45$ .

$30 + \frac{x \cdot 56}{5} \geq 2$

Move $56$ to the left of $x$ .

$30 + \frac{56 x}{5} \geq 2$

Step 4

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

Subtract $30$ from both sides of the inequality.

$\frac{56 x}{5} \geq 2 - 30$

Subtract $30$ from $2$ .

$\frac{56 x}{5} \geq - 28$

Step 5

Multiply both sides by $5$ .

$\frac{56 x}{5} \cdot 5 \geq - 28 \cdot 5$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{56 x}{5} \cdot 5 \geq - 28 \cdot 5$

Rewrite the expression.

$56 x \geq - 28 \cdot 5$

Simplify the right side.

Multiply $- 28$ by $5$ .

$56 x \geq - 140$

Step 7

Divide each term in $56 x \geq - 140$ by $56$ and simplify.

Divide each term in $56 x \geq - 140$ by $56$ .

$\frac{56 x}{56} \geq \frac{- 140}{56}$

Simplify the left side.

Cancel the common factor of $56$ .

Cancel the common factor.

$\frac{56 x}{56} \geq \frac{- 140}{56}$

Divide $x$ by $1$ .

$x \geq \frac{- 140}{56}$

Simplify the right side.

Cancel the common factor of $- 140$ and $56$ .

Factor $28$ out of $- 140$ .

$x \geq \frac{28 (- 5)}{56}$

Cancel the common factors.

Factor $28$ out of $56$ .

$x \geq \frac{28 \cdot - 5}{28 \cdot 2}$

Cancel the common factor.

$x \geq \frac{28 \cdot - 5}{28 \cdot 2}$

Rewrite the expression.

$x \geq \frac{- 5}{2}$

Move the negative in front of the fraction.

$x \geq - \frac{5}{2}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{5}{2}$

Interval Notation:

$[- \frac{5}{2}, \infty)$

Solve the Inequality for x -9x+2<=-3(-4/5x-10)-1/5x

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