Question

How do you solve `-1+ \frac { 10} { 7} x > - 17`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(1)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-1 + color(red)(1) + 10/7x > -17 + color(red)(1)`

`0 + 10/7x > -16`

`10/7x > -16`

Now, multiply each side of the inequality by `color(red)(7)/color(blue)(10)` to solve for `x` while keeping the inequality balanced:

`color(red)(7)/color(blue)(10) xx 10/7x > color(red)(7)/color(blue)(10) xx -16`

`cancel(color(red)(7))/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)))/color(red)(cancel(color(black)(7)))x > color(red)(7)/(cancel(color(blue)(10))5) xx color(blue)(cancel(color(black)(-16)))-8`

`x = 7/5 xx -8`

`x = -56/5`