Solve -43+13rgeq-2(11-3r)-7

$$- 43 + 13 r \geq - 2 ( 11 - 3 r ) - 7$$

Solve for r

$$r\geq 2$$

Solution Steps

Use the distributive property to multiply -2 by 11-3r.

$$-43+13r\geq -22+6r-7$$

Subtract 7 from -22 to get -29.

$$-43+13r\geq -29+6r$$

Subtract 6r from both sides.

$$-43+13r-6r\geq -29$$

Combine 13r and -6r to get 7r.

$$-43+7r\geq -29$$

Add 43 to both sides.

$$7r\geq -29+43$$

Add -29 and 43 to get 14.

$$7r\geq 14$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$r\geq \frac{14}{7}$$

Divide 14 by 7 to get 2.

$$r\geq 2$$