Question

How do you solve and graph `3/4j-10>=5`?

Answer 1

See a solution process below:

Explanation:

Step 1) Add `color(red)(10)` to each side of the inequality to isolate the `j` term while keeping the inequality balanced:

`3/4j - 10 + color(red)(10) >= 5 + color(red)(10)`

`3/4j - 0 >= 15`

`3/4j >= 15`

Step 2) Multiply each side of the inequality by `color(red)(4)/color(blue)(3)` to solve for `j` while keeping the inequality balanced:

`color(red)(4)/color(blue)(3) xx 3/4j >= color(red)(4)/color(blue)(3) xx 15`

`cancel(color(red)(4))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(4)))j >= color(red)(4)/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(15)))5`

`j >= 20`

We can graph this solution as:

graph{x >= 20 [-30, 30, -10, 10]}