Solve the Inequality for r -5r+15>=-5(r-2)

$- 5 r + 15 \geq - 5 (r - 2)$

Step 1

Simplify $- 5 (r - 2)$ .

Rewrite.

$- 5 r + 15 \geq 0 + 0 - 5 (r - 2)$

Simplify by adding zeros.

$- 5 r + 15 \geq - 5 (r - 2)$

Apply the distributive property.

$- 5 r + 15 \geq - 5 r - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$- 5 r + 15 \geq - 5 r + 10$

Step 2

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

Add $5 r$ to both sides of the inequality.

$- 5 r + 15 + 5 r \geq 10$

Combine the opposite terms in $- 5 r + 15 + 5 r$ .

Add $- 5 r$ and $5 r$ .

$0 + 15 \geq 10$

Add $0$ and $15$ .

$15 \geq 10$

Step 3

Since $15 \geq 10$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$