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Let's solve the equation step by step.

The given equation is:

\[
-3(5x - 7) = 3(-5x + 7)
\]

### Step 1: Distribute the numbers
We will first apply the distributive property to both sides:

\[
-3 \cdot 5x + (-3) \cdot (-7) = 3 \cdot (-5x) + 3 \cdot 7
\]

Simplifying both sides:

\[
-15x + 21 = -15x + 21
\]

### Step 2: Simplify the equation
At this point, the equation is:

\[
-15x + 21 = -15x + 21
\]

If we subtract \(-15x\) from both sides, we get:

\[
21 = 21
\]

### Step 3: Interpret the result
Since both sides are equal and the variables cancel out, this means the equation holds true for all values of \(x\).

### Conclusion:
The equation has **infinite solutions**.

Would you like a further explanation on any of the steps? Here are some additional related questions you might find interesting:

1. How do you recognize equations with infinite solutions?
2. Can you provide an example of an equation with no solutions?
3. How do you apply the distributive property in equations?
4. What is the difference between a conditional equation and an identity?
5. How do you handle equations where the variable cancels out?

**Tip**: When solving equations, always simplify both sides first, as it can help reveal the solution faster.

Solve the following equation for x: -3(5x - 7) = 3(-5x + 7). Express your answer in the simplest form. If there are infinite solutions, state 'infinite solutions,' and if there are no solutions, state 'no solutions.'

Step-by-step solution for solving the linear equation -3(5x - 7) = 3(-5x + 7) using the distributive property. Learn how to identify infinite solutions in equations. Ideal for students in Grades 9-10.

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