Question

How do you solve `-3\geq - \frac { 4} { 7} u + 5`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(5)` from each side of the inequality to isolate the `u` term while keeping the inequality balanced:

`-3 - color(red)(5) >= -4/7u + 5 - color(red)(5)`

`-8 >= -4/7u + 0`

`-8 >= -4/7u`

Now, multiply each side of the inequality by `-color(blue)(7)/color(green)(4)` to solve for `u` while keeping the inequality balanced. However, because we are multiply or dividing an inequality by a negative number we must reverse the inequality operator:

`color(blue)(-7)/color(green)(4) xx -8 color(red)(<=) -color(blue)(7)/color(green)(4) xx -4/7u`

`56/4 color(red)(<=) -cancel(color(blue)(7))/cancel(color(green)(4)) xx -color(green)(cancel(color(black)(4)))/color(blue)(cancel(color(black)(7)))u`

`14 color(red)(<=) u`

To state the solution in terms of `x` we can reverse or "flip" the entire inequality:

`u >= 14`