Question

Solve the following inequality:

Answer 1

`r \ge -16`

Explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

`(-10+r)/(2) \ge -13`

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

`(-10+r)/(2) *2 \ge -13 *2`

`-10+r \ge -26`

Add 10 to both sides, and simplify

`(-10+r)+10 \ge (-26)+10`

`r \ge -16`

Answer 2

`r \geqslant - 16`

Explanation:

`( - 10 + r)/(2) \geqslant - 13`

multiply both sides by 2:

`- 10 + r \geqslant - 26`

add 10 on both sides:

`r \geqslant - 16`