Final answer:
To solve the equation, (4/5)x - 2 = (3/10)x + 1, for x, we can start by getting rid of the fractions and then isolate the variable on one side. Solving for x, we find that x = 6.
Step-by-step explanation:
To write and solve the equation, we can let the unknown number be represented by the variable 'x'. The given information states that 'Four-fifths of a number minus two is equal to three-tenths of the same number plus one'. So, we can express this as an equation: (4/5)x - 2 = (3/10)x + 1.
To solve for 'x', we can start by getting rid of the fractions. Multiplying both sides of the equation by 10 and simplifying, we get: 8x - 20 = 3x + 10.
Now, we can solve for 'x' by isolating the variable term on one side and the constant term on the other side. Adding 20 to both sides, we have: 8x = 3x + 30. Next, subtracting 3x from both sides, we get: 5x = 30. Finally, dividing both sides by 5, we find that x = 6.