%2F4%3D(x%2B7)%2F3.jpeg "(2x+3)/4=(x+7)/3")
Solving the Equation: (2x + 3)/4 = (x + 7)/3
This article will guide you through the steps of solving the equation (2x + 3)/4 = (x + 7)/3.
Step 1: Eliminate the fractions
To simplify the equation, we need to eliminate the fractions. We can achieve this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is 12.
12 * [(2x + 3)/4] = 12 * [(x + 7)/3]
This simplifies to:
3(2x + 3) = 4(x + 7)
Step 2: Expand the equation
Now, we expand both sides of the equation by distributing:
6x + 9 = 4x + 28
Step 3: Isolate the x term
To isolate the 'x' term, we need to move all 'x' terms to one side of the equation and all constant terms to the other side. Subtracting 4x from both sides:
6x - 4x + 9 = 4x - 4x + 28
This simplifies to:
2x + 9 = 28
Step 4: Solve for x
Finally, to solve for 'x', we subtract 9 from both sides:
2x + 9 - 9 = 28 - 9
This simplifies to:
2x = 19
Divide both sides by 2:
2x / 2 = 19 / 2
This gives us the solution:
x = 9.5
Conclusion
Therefore, the solution to the equation (2x + 3)/4 = (x + 7)/3 is x = 9.5.