Question

How do you solve `\frac { u } { - 12} + 185\geq 174`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(blue)(185)` from each side of the inequality to isolate the `u` term while keeping the inequality balanced:

`u/(-12) + 185 - color(blue)(185) >= 174 - color(blue)(185)`

`u/(-12) + 0 >= -11`

`u/(-12) >= -11`

Now, multiply each side of the inequality by `color(red)(-12)` to solve for `u` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality operator:

`color(red)(-12) xx u/(-12) color(red)(<=) color(red)(-12) xx -11`

`cancel(color(red)(-12)) xx u/color(red)(cancel(color(black)(-12))) color(red)(<=) 132`

`u <= 132`