Final answer:
To solve the equation 1/2x + 3/4x = 5 - 2.5x, combine like terms and isolate the variable x on one side of the equation. The solution is x = 20/13.
Step-by-step explanation:
To solve the equation 1/2x + 3/4x = 5 - 2.5x, we can combine like terms on the left side of the equation by finding a common denominator for the fractions. The common denominator for 1/2 and 3/4 is 4, so we rewrite the equation as (2/4)x + (3/4)x = 5 - 2.5x.
Simplifying the equation, we get (5/4)x = 5 - 2.5x. Now, we can isolate the variable x by adding 2.5x to both sides of the equation and subtracting 5/4x from both sides.
This gives us (5/4 + 2.5)x = 5, and simplifying further, we have (13/4)x = 5. To solve for x, we divide both sides of the equation by 13/4, which is the same as multiplying by the reciprocal. Thus, x = 5 / (13/4), which is equivalent to x = 20/13.