Algebra, I asked and didn't understand the answer...?

Question

I thought I had this, I asked to check and became more confused. Can someone please help me with this? (explain a little the order maybe)...

Solve for x:
(2x – 5)/3 – 3/2 = (x + 4)/5

Answer 1

The first thing that you need to do is separate out the fractions. This can be done by multiplying both sides of the equation by 30 (elliminating the fractions altogether) or you can separate the numerators by themselves. This is done by (2x-5)/3=2x/3-5/3 and similarly for the other fraction. I think that it is easier to just get rid of the fractions.

When you multiply by 30 on both sides, the equation becomes:
10(2x-5)-45=6(x+4).
You then multiply to elliminate the parathesis:
20x-50-45=6x+24.
Combine the like terms (All the x's on one side and all the numbers on the other)
20x-6x=50+45+24
14x=119
x=119/14=17/2. This fraction doesn't simplify further without decimals.

Answer 2

You have to multiply by all of the denominators.
5(2x-5)/3 - 5(3/2) = (x + 4)
10(2x - 5)/3 - 5(3) = 2(x + 4)
10(2x - 5) - 15(3) = 6(x + 4)
Then you multiply the numbers through
20x - 50 - 45 = 6x + 24
20x - 95 = 6x +24
Then get everything with x to one side and everything without to the other side.
20x = 6x +119
14x = 119
now divide both sides by 14
x = (119/14)
x = 8.5

Answer 3

Well, I don't know how the other person did it.... but I can show you this way...

First, I would get rid of all the denomintors by multiplying each thing by 30 (a number that will divide each denom evenly)

So, you get 30(2x-5)/3 - 30(3/2) = 30(x+4)/5

Now, you can divide each 30 by each denominator.. eg. 30 divided by 3 leaves 10 on top

10(2x-5) - 45 = 6(x+4)

Now, multiply the 10 and 6 through their brackets

20x-50 - 45 = 6x + 24

Now, just move all the x things to left, all the non-x things to right. To move something to the other side, you just make it the opposite operation (- becomes +, + becomes -)

20x -6x = 24 +50 + 45
14x = 119
Now you get rid of the 14 by taking it over to the right and making it the opposite operation (times becomes divide)

x=119/14
x=8.5

Answer 4

Solve for x: (2x - 5)/3 - 3/2 = (x + 4)/5

First: eliminate fractions - multiply the denominators with each term....

(3)(2)(5)((2x-5)/3)-(3)(2)(5)(3/2)=(3)(2)(5)((x+4)/5)

*Cross cancel "like" terms & combine the remaining terms....

(2)(5)(2x - 5) - 15(3) = (3)(2)(x + 4)

10(2x - 5) - 45 = 6(x + 4)

Sec: distribute the outer terms with terms in parenthesis....

10(2x)+10(-5) - 45=6(x)+6(4)

20x + (-50) - 45 = 6x + 24

20x - 50 - 45 = 6x + 24

20x - 95 = 6x + 24

*Add "95" with both sides (when you move a term to the opposite side, always use the opposite sign)....

20x - 95 + 95 = 6x + 24 + 95

20x = 6x + 24 + 95

20x = 6x + 119

*Subtract 6x from both sides....

20x - 6x = 6x - 6x + 119

20x - 6x = 119

14x = 119

Third: isolate "x" on one side - divide both terms by 14....

14x/14 = 119/14

x = 119/14

Answer 5

You expand it a bit... Above eqn can be written as

2x/3 - 5/3 - 3/2 = x/5 + 4/5

Get all x'es together

2x/3-x/5 = 5/3+3/2+4/5

(10x - 3x)/15 = (50+45+24)/30 = 119/30

7x/15 = 119/30
7x= 119/2

x = 119/14

Answer 6

(2x-5)/3 - 3/2 = (x+4)/5

Expand it out

2/3 X - 5/3 - 3/2 = 1/5 x + 4/5

Multiple everything by 3...

2X - 5 - 9/2 = 3/5 X + 12/5

Multiply everything by 5

10 X - 25 - 45/2 = 3X + 12

Multiply everything by 2

20X - 50 - 45 = 6X + 24
20X - 95 = 6x + 24
14X = 119
X = 119/14 = 8.5

Answer 7

(2x-5)/3 -3/2 = (x+4)/5 Let's multiply both sides by 60 to get rid of the fractions:

20(2x-5) - 90 = 12(x+4) Expand terms again:

40x - 100 - 90 = 12x + 48 =

40x - 190 = 12x + 48 =

28x = 238
14x = 119
2x = 17
x = 17/2

Answer 8

a million. to circulate from a y interior the denominator to a y^2 interior the denominator, you will desire to multiply via y/y, which equals a million so it would not replace the subject in any way, so the respond would via 7y/y^2 2.For this one you will desire to have a common denominator, the least common denominator of 6 and 7 is 40 two, so which you will desire to make each and each fraction over 40 two, to try this for the 1st one you will desire to multiply via 6/6, and for the 2nd you will desire to multiply via 7/7, the 1st one would be 36/40 two and the 2nd would be 40 9/40 two. The equation would be 36/40 two-40 9/40 two. the respond would then come out as -13/40 two 3. ok so for this one you will desire to circulate multiply the equation. to try this you multiply the suitable one on the left via the backside one on the excellent and set it equivalent to multiplying the backside left via the suitable appropriate. this would be -8x=7, then you definately would desire to divide the two factors via -8 to isolate the x, the respond would then be -7/8 4. you will desire to subtract 10.8x-4.9x first, this would consequence in 5.9x and set that equivalent to -177, so 5.9x=-177. Now you will desire to divide the two factors via 5.9 to isolate the x, So x= -30 5. This one is definitely the least confusing out of all of them, you will desire to easily upload the xs with the xs and the ys with the ys, so 5.9x+.96x +.68y+4y the respond would then be 6.86x+4.68y i'm hoping this facilitates

Answer 9

(2x – 5)/3 – 3/2 = (x + 4)/5
Common denominator on left side = 6

4x - 19 / 6 = (x+4)/5
Multiply left side by 5 and right side by 6 (i.e cross multiply)

20x - 95 = 6x + 24
Isolate for variable on one side

14x = 119
divide both sides by 14

[[ x = 8.5 ]]