Final answer:
To solve the equation 2/3 x - 1/5 x = x - 1, we first combine like terms and then isolate x by subtracting x from both sides and dividing both sides by the coefficient of x, resulting in x = 15/8.
Step-by-step explanation:
We first need to combine like terms by finding a common denominator for the x terms on the left-hand side. Combining fractions, we get:
10/15 x - 3/15 x = x - 1
(10 - 3)/15 x = x - 1
7/15 x = x - 1
Now, to isolate x, we subtract x from both sides:
7/15 x - x = -1
To combine the x terms, convert 1 x to 15/15 x:
7/15 x - 15/15 x = -1
(7 - 15)/15 x = -1
-8/15 x = -1
To find the value of x, divide both sides by -8/15, which is the same as multiplying by the reciprocal -15/8:
x = -1 * (-15/8)
x = 15/8