What is the value of x in the equation 4(3/10) - (2(2/5)x + 5(1/2)) = (1/2)(-3(3/5)x + 1(1/5))?

 Firstly, let's simplify the equation step by step.

The equation is 4(3/10) - (2(2/5)x + 5(1/2)) = (1/2)(-3(3/5)x + 1(1/5)).

We'll handle each term individually:

For the left side: 1. Simplify 4(3/10) = 4 * 3/10 = 12/10 = 1.2 2. Simplify 2(2/5)x = 2 * 2/5 x = 4/5 x 3. Simplify 5(1/2) = 5 * 1/2 = 5/2 = 2.5

Now, the left side is: 1.2 - (4/5)x - 2.5

For the right side: 1. Simplify -3(3/5)x = -3 * 3/5 x = -9/5 x 2. Simplify 1(1/5) = 1 * 1/5 = 1/5

Now, multiply the entire right side by 1/2: (1/2)(-9/5 x + 1/5) = -9/10 x + 1/10

Now our equation is: 1.2 - (4/5)x - 2.5 = -9/10 x + 1/10

Combine like terms on the left side: 1.2 - 2.5 = -1.3 Now we have -1.3 - (4/5)x = -9/10 x + 1/10

Next, we want to get all the x terms to one side and the constants to the other side. To do this, add (4/5)x to both sides and add 1.3 to both sides:

-1.3 + 1.3 - (4/5)x + (4/5)x = 1.3 + -9/10 x + (4/5)x + 1/10

Simplifying that we get: 0 = 1.4 + (-9/10 + 4/5) x

Since 4/5 is 8/10, we can combine the x terms: 1.4 + (-9/10 + 8/10) x = 1.4 - 1/10 x

Now we want to solve for x, so we subtract 1.4 from both sides: 0 - 1.4 = -1.4 = -1/10 x

Now, we divide both sides by -1/10 to solve for x: x = (-1.4) / (-1/10) x = 14

So the value of x is 14.