Question

Solve the linear inequality:
5 - 5/3x (greater than equal to sign inserted) 9
Sorry I cannot insert the greater than equal to sign into the equation.

Answer 1

so you have

\[5 - \frac{5}{3x} \ge 9\]

start by subtracting 5 from both sides

them multiply both sides by 3x

this should make it easier for you to solve

Answer 2

If you multiply both sides by 3x how do you know if you are multiplying by a negative or positive number? Should you switch the inequality symbol or not?

Answer 3

well you would have \[-5 \ge 12x\]
I hope that make sense...

Answer 4

Campbell, that is what I got when I multiplied, so would that be the solution set?

Answer 5

well there are lots of methods from here...

the easiest to understand is to now

1. subtract 12x from both sides

2. add 5 to both sides..

now the inequality will read from left to right as we are normally use to

do you know about the inequality and dividing by a negative..?

Answer 6

No, I do not I have not done inequalities in forever, which is why I am so confused.

Answer 7

I am confused, instead of adding or subtracting wouldn't you divide -5 in 12x? If I am wrong please let me know, as I said I haven't worked on inequalities in so long

Answer 8

well you would have

\[-12x \ge 5\]

dividing by a negative requires you to reverse the inequality

so divide by -12

Answer 9

\[5-\frac{5}{3x}\ge9\]
\[\frac{-5}{3x}-4\ge0\]
\[\frac{-5-12x}{3x}\ge0\]

Answer 10

The numerator is 0 if x = -5/12
The denominator is 0 if x = 0

Answer 11

Campbell wouldn't that give you just -5/12 ?
Oh man now I am really confused.

Answer 12

so \[x \le -\frac{5}{12}\]

Answer 13

Thats what I got, because you need to reserve the sign as well right? I think I am getting this, at least I hope