# Solve the inequality (x-6)/2 - (x-4)/5 <= -x/4

#### spooky1

##### New member
(x - 6)/2 - (x - 4)/5 < -x/4

#### stapel

##### Super Moderator
Staff member
spooky1 said:
(x - 6)/2 - (x - 4)/5 < -x/4
Since you don't have a value for "x", you can't multiply or divide through by anything involving x: you don't know if you'd need to flip the inequality.

Instead, start by adding x/4 over to the left-hand side. Convert the fractions to the common denominator of 20, and combine. Then note that you have a positive denominator, so the fraction will be negative when the numerator is negative, and the fraction will be zero when the numerator is zero.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

#### spooky1

##### New member
Solve the inequality

I got x < 4

#### tkhunny

##### Moderator
Staff member
How did you manage to enter the first equation so beautifully and this one so badly?

That is a good answer, but one has a difficult time knowing how you arrived at it.

#### spooky1

##### New member
Solve the inequality

Well excuse me.
1. I multiplied each term by 20
2. 10x-60-4x-16<=-5x
3. 6x-44<=-5x
4. 11x<=44
5. x<=4

#### stapel

##### Super Moderator
Staff member
Re: Solve the inequality

spooky1 said:
I multiplied each term by 20
10x - 60 - 4x - 16 <= -5x
Don't try to do too much at once:

. . . . .20[(x - 6)/2] - 20[(x - 4)/5] < 20[-x/4]

. . . . .10(x - 6) - 4(x - 4) < 5(-x)

. . . . .10x - 60 - 4x + 16 < -5x

spooky1 said:
6x-44=-5x
But -60 + (-16) = -76, not -44. (Errors don't usually "cancel out", so it's generally better to do the computations correctly the whole way through.)

Eliz.

#### spooky1

##### New member
Solve the inequality

I entered my solution steps wrong. I corrected the posting.

1. 10x-60-4x+16<=-5x
2. 6x-44<=-5x
3. 11x<=44
4. x<=4

#### tkhunny

##### Moderator
Staff member
No need to take things personally. Just answer the objections and let's all learn together.