help on a math problem!?

Question

dont understand? Solve for x: 1/5x - 2 ≥ 3/4x + 5
came up with 3 answers
1.x ≤ -140/11
2.≥ -140/11
3.x ≥ 140/11

Answer 1

(1/5)x - 2 ≥ (3/4)x + 5
Multiply everything by 20
4x - 40 ≥ 15x + 100
Add 40 to each side
4x ≥ 15x + 140
Subtract 15x from each side
-11x ≥ 140
Divide each side by -11 (notice that the inequality flips)
x ≤ 140/-11 or x ≤ -140/11

Answer 2

Let's see. I'm not too sure whether you mean (1/5)x and (3/4)x or 1/(5x) and 3/(4x).

If you mean the first, all you need to do is isolate x. You have:

(1/5)x - 2 ≥ (3/4)x + 5
-2 ≥ (11/20)x + 5
-7 ≥ (11/20)x
-140/11 ≥ x

in which case the sign never changes because you only add and subtract and multiply by a positive number (e.g. 20/11)

Of course, if instead, you mean:

1/(5x) - 2 ≥ 3/(4x) + 5

We have two cases: x > 0 and x < 0. x ≠ 0 because otherwise the denominator would be 0.

If x > 0, we multiply by the LCD = 20x. Because it's positive, we don't change signs:

4 - 40x ≥ 15 + 100x
-11 ≥ 140x
-11/140 ≥ x

and there is no answer because

{x | x > 0} U {x | x ≤ -11/140} = Ø

meaning x cannot be greater than 0 (our assumption) and less than or equal to -11/140

In the second case, if x < 0, we have:

4 - 40x ≤15 + 100x (sign changes because 20x < 0!)
-11 ≤ 140x
-11/140 ≤ x

in which case we have:

{x | x < 0} U {x | x ≥ -11/140} = {x | -11/140 ≤ x < 0}

And our answer is any number in which

-11/140 ≤ x < 0

Answer 3

Testing the answers:
With (+140/11)
(1/5)(+140/11) - 2 = .54545
(3/4)(+140/11) +5 =14.545454

With (-140/11)
(1/5)(-140/11) - 2 = -4.54545
(3/4)(-140/11) +5 = -4.545454

So (-140/11) satisfies the "=" requirement
Now for less-than or greater-than:
(-141/11) is < (-140/11) and
(1/5)(-141/11) - 2 = -4.5636 which is > (3/4)(-141/11)+5 = -4.61364

So x <= (-140/11) looks correct to me.

Answer number 1

Answer 4

1/5(x) - 2 ≥ 3/4(x) + 5
1/5(x) - 3/4(x) ≥ 7

1/5, 3/4
1/5 = 4/20
3/4 = 15/20

4/20(x) - 15/20(x) ≥ 7
-11/20(x) ≥ 7/1

x ≤ (7) / [-11/20]
x ≤ [7/1] * [20/-11]
x ≤ 140/-11

x ≤ -140 / 11

So, the answer is #1.

Answer 5

the first one is correct...

x ≤ -140/11

Answer 6

I think it's true or false depending on the value of x

Answer 7

answer 1 is what i got

Answer 8

3... definately

Answer 9

The answer is purple.

Answer 10

number one. this one i solved in my head easily...