Solve this equation for x: 3x-(5x-9)=7-4(x+1)

Let's solve the equation step by step:

The given equation is:
\[
3x - (5x - 9) = 7 - 4(x + 1)
\]

### Step 1: Distribute and simplify
First, distribute the negative sign on the left side and the 4 on the right side:

\[
3x - 5x + 9 = 7 - 4x - 4
\]

### Step 2: Combine like terms
Next, combine the like terms on both sides of the equation:

On the left side:
\[
(3x - 5x) + 9 = -2x + 9
\]

On the right side:
\[
7 - 4 = 3 \Rightarrow 3 - 4x
\]

So, the equation now is:
\[
-2x + 9 = 3 - 4x
\]

### Step 3: Get all terms involving x on one side
To isolate \( x \), add \( 4x \) to both sides:

\[
-2x + 4x + 9 = 3 - 4x + 4x
\]

Simplifying further:
\[
2x + 9 = 3
\]

### Step 4: Isolate \( x \)
Subtract 9 from both sides to isolate the \( x \) term:

\[
2x = 3 - 9 \Rightarrow 2x = -6
\]

Finally, divide by 2 to solve for \( x \):

\[
x = \frac{-6}{2} \Rightarrow x = -3
\]

### Final Answer:
\[
x = -3
\]

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

Here are 5 related questions to further explore:

1. What would happen if the equation had an additional constant term on one side?
2. How can you verify the solution \( x = -3 \) is correct?
3. How do you solve similar equations that involve fractions?
4. What is the effect of distributing a negative sign through parentheses?
5. How can this equation be graphed to visually confirm the solution?

**Tip:** Always simplify the equation as much as possible before trying to isolate the variable. This reduces the chances of making errors.

Learn how to solve the equation 3x - (5x - 9) = 7 - 4(x + 1) step-by-step with a detailed solution. This problem covers key algebraic concepts such as equations, distributive property, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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