To solve the equation 2/5 + 3x/5 = (x + 5)/10, we need to eliminate the fractions by finding a common denominator. The least common multiple of 5 and 10 is 10.
First, we can rewrite each term with a denominator of 10:
- For 2/5, we multiply by 2 to get 4/10.
- For 3x/5, we also multiply by 2 to get 6x/10.
- The right side (x + 5)/10 stays the same.
This gives us the new equation:
4/10 + 6x/10 = (x + 5)/10
Now, we can eliminate the denominators by multiplying the entire equation by 10:
10 * (4/10) + 10 * (6x/10) = 10 * ((x + 5)/10)
This simplifies to:
4 + 6x = x + 5
Next, we want to get all terms involving x on one side and constants on the other. Start by subtracting x from both sides:
4 + 6x – x = 5
This simplifies to:
4 + 5x = 5
Now, subtract 4 from both sides:
5x = 5 – 4
This gives:
5x = 1
Finally, divide both sides by 5:
x = 1/5
So the solution to the equation is x = 1/5.