The equation you've written is:

\[
125x + 7 = 25(3x - 4)
\]

Let's solve this step by step:

### Step 1: Expand the right-hand side of the equation
We expand the term \(25(3x - 4)\):

\[
125x + 7 = 25 \cdot 3x - 25 \cdot 4
\]
\[
125x + 7 = 75x - 100
\]

### Step 2: Move all terms involving \(x\) to one side
To do this, subtract \(75x\) from both sides:

\[
125x - 75x + 7 = -100
\]
\[
50x + 7 = -100
\]

### Step 3: Move constant terms to the other side
Subtract 7 from both sides:

\[
50x = -100 - 7
\]
\[
50x = -107
\]

### Step 4: Solve for \(x\)
Now, divide both sides by 50:

\[
x = \frac{-107}{50}
\]

Thus, the solution is:

\[
x = -\frac{107}{50} \quad \text{or} \quad x = -2.14
\]

Would you like more details on any of these steps or have any further questions?

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Here are 5 related questions you can explore:

1. How do you solve linear equations with variables on both sides?
2. What happens when the solution to an equation is a fraction?
3. How do you expand and simplify expressions in algebra?
4. How do you check if your solution to an equation is correct?
5. What is the significance of balancing both sides of an equation?

**Tip:** Always check your solution by plugging it back into the original equation to verify it works!

Learn how to solve the linear equation 125x + 7 = 25(3x - 4) step by step. This problem involves the distributive property and solving for x when variables are on both sides. Ideal for students in Grades 8-10.

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