Solve -2(9r+3)-7rgeq-10r-(12r+9)

$$- 2 ( 9 r + 3 ) - 7 r \geq - 10 r - ( 12 r + 9 )$$

Solve for r

$$r\leq 1$$

Solution Steps

Use the distributive property to multiply -2 by 9r+3.

$$-18r-6-7r\geq -10r-\left(12r+9\right)$$

Combine -18r and -7r to get -25r.

$$-25r-6\geq -10r-\left(12r+9\right)$$

To find the opposite of 12r+9, find the opposite of each term.

$$-25r-6\geq -10r-12r-9$$

Combine -10r and -12r to get -22r.

$$-25r-6\geq -22r-9$$

Add 22r to both sides.

$$-25r-6+22r\geq -9$$

Combine -25r and 22r to get -3r.

$$-3r-6\geq -9$$

Add 6 to both sides.

$$-3r\geq -9+6$$

Add -9 and 6 to get -3.

$$-3r\geq -3$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

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

Divide -3 by -3 to get 1.

$$r\leq 1$$