Solve the Inequality for r r+5(-2r-10)<=-4r-1+6r

$r + 5 (- 2 r - 10) \leq - 4 r - 1 + 6 r$

Simplify $r + 5 (- 2 r - 10)$ .

Simplify each term.

Apply the distributive property.

$r + 5 (- 2 r) + 5 \cdot - 10 \leq - 4 r - 1 + 6 r$

Multiply $- 2$ by $5$ .

$r - 10 r + 5 \cdot - 10 \leq - 4 r - 1 + 6 r$

Multiply $5$ by $- 10$ .

$r - 10 r - 50 \leq - 4 r - 1 + 6 r$

Subtract $10 r$ from $r$ .

$- 9 r - 50 \leq - 4 r - 1 + 6 r$

Add $- 4 r$ and $6 r$ .

$- 9 r - 50 \leq 2 r - 1$

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

Subtract $2 r$ from both sides of the inequality.

$- 9 r - 50 - 2 r \leq - 1$

Subtract $2 r$ from $- 9 r$ .

$- 11 r - 50 \leq - 1$

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

Add $50$ to both sides of the inequality.

$- 11 r \leq - 1 + 50$

Add $- 1$ and $50$ .

$- 11 r \leq 49$

Divide each term in $- 11 r \leq 49$ by $- 11$ and simplify.

Divide each term in $- 11 r \leq 49$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 r}{- 11} \geq \frac{49}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 r}{- 11} \geq \frac{49}{- 11}$

Divide $r$ by $1$ .

$r \geq \frac{49}{- 11}$

Simplify the right side.

Move the negative in front of the fraction.

$r \geq - \frac{49}{11}$

The result can be shown in multiple forms.

Inequality Form:

$r \geq - \frac{49}{11}$

Interval Notation:

$[- \frac{49}{11}, \infty)$

Solve the Inequality for r r+5(-2r-10)<=-4r-1+6r

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