Final answer:
To solve for x in the expression 4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5), simplify the equation by converting mixed numbers to fractions, distribute the fractions, combine like terms, and isolate the variable.
Step-by-step explanation:
To solve for x in the expression 4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5), we need to simplify the equation step by step.
First, let's simplify the fractions in the equation. Convert the mixed numbers to improper fractions:
4 3/10 = 43/10, 2 2/5 = 12/5, and 5 1/2 = 11/2.
Now, distribute the fractions inside the parentheses:
4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5)
43/10 - (12/5x + 11/2) = (1/2)(-18/5x + 6/5)
Simplify further:
43/10 - (12/5x + 11/2) = -9/5x + 3/5
Next, combine like terms:
43/10 - (24/10x + 55/10) = -9/5x + 3/5
43/10 - 79/10 - 24/10x = -9/5x + 3/5
-36/10x = -9/5x + 3/5
To get rid of the denominators, multiply both sides by 10:
-36x = -18x + 6
Now, let's isolate the variable:
-36x + 18x = 6
-18x = 6
Divide both sides by -18:
x = -6/18
Simplify the fraction:
x = -1/3
So, the value of x in the expression is -1/3.