Question

How do you solve the inequality `-5-x/6> -9`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(5)` to each side of the inequality to isolate the `x` term while keeping the inequality balanaced:

`-5 + color(red)(5) - x/6 > -9 + color(red)(5)`

`0 - x/6 > -4`

`-x/6 > -4`

Now, multiply each side of the inequality by `color(blue)(-6)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`color(blue)(-6) xx -x/6 color(red)(<) color(blue)(-6) xx -4`

`(color(blue)(6)x)/6 color(red)(<) 24`

`(cancel(color(blue)(6))x)/color(blue)(cancel(color(black)(6))) color(red)(<) 24`

`x < 24`

Answer 2

`x<24`

Explanation:

When working with inequalities it is a good idea to work with a positive variable term. This avoids problems with the inequality sign,

`-5color(blue)(-x/6) > color(red)(-9)`

Move the `color(blue)(-x/6)` term to the right side and the `color(red)(-9)` to the left.

(Add `x/6 and 9` to both sides)

#-5" "color(red)(+9)" "color(blue)(-x/6 +x/6) > color(red)(-9 +9) ""color(blue)(+x/6)#

`" "4 > x/6" "larr ( xx 6)`

`" "24 >x`

This is the same as `x<24`