Step 1: Understand the Equation
The equation given is:
7x - 4 = 5x + 3
This is a linear equation in one variable (x). The goal is to isolate x on one side of the equation.
Step 2: Rearranging the Equation
To solve for x, we need to get all the x terms on one side and the constant terms on the other side. We can start by subtracting 5x from both sides:
- 7x - 5x - 4 = 3
- This simplifies to:
2x - 4 = 3
Step 3: Isolate the x Term
Next, we need to isolate the term with x. To do this, add 4 to both sides:
- 2x - 4 + 4 = 3 + 4
- This simplifies to:
2x = 7
Step 4: Solve for x
Now, divide both sides by 2 to solve for x:
- 2x / 2 = 7 / 2
- This simplifies to:
x = 3.5
Step 5: Conclusion
The solution to the equation 7x - 4 = 5x + 3 is:
- x = 3.5
This means that when x equals 3.5, both sides of the original equation are equal. You can verify this by substituting x back into the original equation.