Final answer:
To solve for x in the equation 4/3/10-(2/2/5+51/2)=1/2(-3/3/5x+1/15), simplify and isolate x. The value of x is 150.
Step-by-step explanation:
To solve for x in the equation 4/3/10-(2/2/5+51/2)=1/2(-3/3/5x+1/15), we need to simplify and isolate x.
First, let's simplify the equation on both sides. On the left side, 4/3/10 is equivalent to 4/(3/10) which is equal to 4 * 10/3 = 40/3. And (2/2/5+51/2) is equal to (2/(2/5) + 51/2) = 2 * 5/2 + 51/2 = 5 + 51/2 = 57/2.
Now, we can rewrite the equation as (40/3) - (57/2) = 1/2(-3/3/5x + 1/15).
Next, we simplify further. On the left side, we can find a common denominator of 6 and rewrite the equation as (40/3)(2/2) - (57/2)(3/3) = 1/2(-3/3/5x + 1/15).
This simplifies to (80/6) - (171/6) = -3/30x + 1/30.
Combining the fractions on the left side, we get (80 - 171)/6 = -3/30x + 1/30.
Simplifying further, we have -91/6 = -3/30x + 1/30.
To isolate x, let's subtract 1/30 from both sides: -91/6 - 1/30 = -3/30x.
This simplifies to -91/6 - 1/30 = -3/30x.
Multiplying both sides by -30/3 to get rid of the fraction on the right side, we have (-91/6 - 1/30)(-30/3) = (-3/30x)(-30/3).
This simplifies to (5/1)(30/1) = x.
Therefore, the value of x in the equation is 150.