Solve the Inequality for r -5r+2(-3r+5)>=-2r-8+3r

$- 5 r + 2 (- 3 r + 5) \geq - 2 r - 8 + 3 r$

Step 1

Simplify $- 5 r + 2 (- 3 r + 5)$ .

Simplify each term.

Apply the distributive property.

$- 5 r + 2 (- 3 r) + 2 \cdot 5 \geq - 2 r - 8 + 3 r$

Multiply $- 3$ by $2$ .

$- 5 r - 6 r + 2 \cdot 5 \geq - 2 r - 8 + 3 r$

Multiply $2$ by $5$ .

$- 5 r - 6 r + 10 \geq - 2 r - 8 + 3 r$

Subtract $6 r$ from $- 5 r$ .

$- 11 r + 10 \geq - 2 r - 8 + 3 r$

Step 2

Add $- 2 r$ and $3 r$ .

$- 11 r + 10 \geq r - 8$

Step 3

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

Subtract $r$ from both sides of the inequality.

$- 11 r + 10 - r \geq - 8$

Subtract $r$ from $- 11 r$ .

$- 12 r + 10 \geq - 8$

Step 4

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

Subtract $10$ from both sides of the inequality.

$- 12 r \geq - 8 - 10$

Subtract $10$ from $- 8$ .

$- 12 r \geq - 18$

Step 5

Divide each term in $- 12 r \geq - 18$ by $- 12$ and simplify.

Divide each term in $- 12 r \geq - 18$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 r}{- 12} \leq \frac{- 18}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 r}{- 12} \leq \frac{- 18}{- 12}$

Divide $r$ by $1$ .

$r \leq \frac{- 18}{- 12}$

Simplify the right side.

Cancel the common factor of $- 18$ and $- 12$ .

Factor $- 6$ out of $- 18$ .

$r \leq \frac{- 6 (3)}{- 12}$

Cancel the common factors.

Factor $- 6$ out of $- 12$ .

$r \leq \frac{- 6 \cdot 3}{- 6 \cdot 2}$

Cancel the common factor.

$r \leq \frac{- 6 \cdot 3}{- 6 \cdot 2}$

Rewrite the expression.

$r \leq \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$r \leq \frac{3}{2}$

Interval Notation:

$(- \infty, \frac{3}{2}]$

Solve the Inequality for r -5r+2(-3r+5)>=-2r-8+3r

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