Solve the Inequality for r r-4(-5r+6)<=4r+10-9

$r - 4 (- 5 r + 6) \leq 4 r + 10 - 9$

Step 1

Simplify $r - 4 (- 5 r + 6)$ .

Simplify each term.

Apply the distributive property.

$r - 4 (- 5 r) - 4 \cdot 6 \leq 4 r + 10 - 9$

Multiply $- 5$ by $- 4$ .

$r + 20 r - 4 \cdot 6 \leq 4 r + 10 - 9$

Multiply $- 4$ by $6$ .

$r + 20 r - 24 \leq 4 r + 10 - 9$

Add $r$ and $20 r$ .

$21 r - 24 \leq 4 r + 10 - 9$

Step 2

Subtract $9$ from $10$ .

$21 r - 24 \leq 4 r + 1$

Step 3

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

Subtract $4 r$ from both sides of the inequality.

$21 r - 24 - 4 r \leq 1$

Subtract $4 r$ from $21 r$ .

$17 r - 24 \leq 1$

Step 4

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

Add $24$ to both sides of the inequality.

$17 r \leq 1 + 24$

Add $1$ and $24$ .

$17 r \leq 25$

Step 5

Divide each term in $17 r \leq 25$ by $17$ and simplify.

Divide each term in $17 r \leq 25$ by $17$ .

$\frac{17 r}{17} \leq \frac{25}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 r}{17} \leq \frac{25}{17}$

Divide $r$ by $1$ .

$r \leq \frac{25}{17}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$r \leq \frac{25}{17}$

Interval Notation:

$(- \infty, \frac{25}{17}]$