Question

How do you solve `-7x - 5> 4x + 50`?

Answer 1

See a solution process below:

Explanation:

Step 1) Add `color(red)(7x)` and subtract `color(blue)(50)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`color(red)(7x) - 7x - 5 - color(blue)(50) > color(red)(7x) + 4x + 50 - color(blue)(50)`

`0 - 55 > (color(red)(7) + 4)x + 0`

`-55 > 11x`

Step 2) Divide each side of the inequality by `color(red)(11)` to solve for `x` while keeping the inequality balanced:

`-55/color(red)(11) > (11x)/color(red)(11)`

`-5 > (color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11))`

`-5 > x`

We can now reverse or "flip" the entire inequality to state the solution in terms of `x`:

`x < -5`