Solving the Equation: 3(2x)/3 + 1 = (7x)/15 + 3
In this article, we will solve the equation 3(2x)/3 + 1 = (7x)/15 + 3. We will break down the equation into smaller parts, simplify each side, and finally find the value of x.
Step 1: Simplify the Left Side
The left side of the equation is 3(2x)/3 + 1. We can simplify this by canceling out the 3 in the numerator and denominator.
3(2x)/3 = 2x
So, the left side becomes:
2x + 1
Step 2: Simplify the Right Side
The right side of the equation is (7x)/15 + 3. We can't simplify this further, so we will leave it as is.
Step 3: Equate the Two Sides
Now that we have simplified both sides, we can equate them:
2x + 1 = (7x)/15 + 3
Step 4: Solve for x
To solve for x, we need to get rid of the fraction on the right side. We can do this by multiplying both sides by 15, which is the denominator of the fraction.
15(2x + 1) = 7x + 45
Expanding the left side, we get:
30x + 15 = 7x + 45
Step 5: Isolate x
Now, we need to isolate x. We can do this by subtracting 15 from both sides and then subtracting 7x from both sides.
30x - 7x = 45 - 15
23x = 30
x = 30/23
Conclusion
Therefore, the value of x is 30/23. We have successfully solved the equation 3(2x)/3 + 1 = (7x)/15 + 3.
