How do you solve this? 1/2x - 1/3 = 3/4x - 3/2?

Is that supposed to be (1/2)x - (1/3) = (3/4)x - (3/2)? Or 1/(2x) - (1/3) - 3/(4x) - 3/2, or something else?

If it's the first one, then just add 1/3 to both sides, then subtract 3/4 from both sides. As you learned back in 3rd grade, you add or subtract fractions by changing the denominators to be the same, then add or subtract the numerators, etc.:

(1/2)x - (3/4)x = (1/3) - (3/2)

(2/4)x - (3/4)x = (2/6) - (9/6)

-(1/4)x = -7/6

x = (-7/6) * (-4)

x = 28/6

x = 14/3

You could alternatively start out by multiplying both sides by the common denominator of 12, which leaves you with 6x - 4 = 9x - 18. You'll get the same solution.

Disagree with siberian. this could artwork with particular equations, yet you're forgetting that as quickly as you're taking the sq. root of a few thing, the respond's the two beneficial and detrimental. utilising 2 plus-minus indicators in an equation like this is discouraged. The evidence is that for the period of this equation, you will in elementary terms get one answer the place 2 are necessary. in case you're taking the sq. root of the two components of (2x ? 4)² = (x + 3)², you would be left with ±(2x ? 4) = ±(x + 3). the subsequent step is kinda difficult to wager. one ought to assert that this equation spilts into (±(2x ? 4) = x + 3) v (2x ? 4 = ±(x + 3)) (±2x ± ?4 = x + 3) v (2x ? 4 = ±x ± 3) (?x ± 2x = 3 ± 4) v (2x ± ?x = 4 ± 3) ({a million, ?3}x = {7, ?a million}) v ({a million, 3}x = {7, a million}) x = {a million/3, 7} yet this is lots messier and complicated than what others stated.

So the question is 1/2x-1/3= 3/4x-3/2

Add 3/2 to each side, resulting in 1/2x+7/6=3/4x

Then substract 1/2x from each side, endng with 7/6= 1/4x

Multiply 4 to each side, and get 28/6 = x

A simplied version is 14/3

1/2x - 1/3 = 3/4x - 3/2

1/2x - 3/4x = 1/3 - 3/2

- 1/4x = - 7/6

-(4/1)1/4x = -(4/1)7/6

- x = - 14/3

or

x = 4 2/3.

re-arrange

1/2x - 3/4x = 1/3 - 3/2

-x/4 = -7/6

-6x = -28

x = 14/3

1/2x - 1/3 = 3/4x - 3/2

x = 14/3

(½)x - (1/3) = (3/4)x - (3/2)

Bring (½)x to the right:

-(1/3) = (3/4)x - (½)x - (3/2)

-(1/3) = (¼)x - (3/2)

Bring -3/2 to the left:

-(1/3) + (3/2) = (��)x

7/2 = (¼)x

Multiply both sides by 4:

(7/6)(4) = (¼)x(4)

x = 14/3

I hope this helps!