Final answer:
To solve the equation - 2/5x + 3 = 2/3x + 1/3, multiply both sides by the least common denominator, combine like terms, and isolate the variable x. The solution is x = 2.5.
Step-by-step explanation:
To solve the equation - 2/5x + 3 = 2/3x + 1/3, we need to combine like terms and isolate the variable x. First, let's get rid of the fractions by multiplying both sides of the equation by the least common denominator, which is 15. This gives us:
15(-2/5x + 3) = 15(2/3x + 1/3)
Simplifying, we have:
-6x + 45 = 10x + 5
Next, we will combine the x terms on one side of the equation and the constant terms on the other side. Subtracting 10x from both sides and adding 45 to both sides, we get:
-16x = -40
Finally, we can solve for x by dividing both sides of the equation by -16:
x = -40/-16
Dividing the numerator and denominator by the greatest common divisor, we have:
x = 10/4 or x = 2.5