Let's solve the equation step by step.

The given equation is:

\[
4(3x - 1) - 4x + 5 = -7
\]

### Step 1: Distribute the 4 across the terms inside the parentheses.
\[
4 \times 3x - 4 \times 1 - 4x + 5 = -7
\]
\[
12x - 4 - 4x + 5 = -7
\]

### Step 2: Combine like terms on the left side.
\[
(12x - 4x) + (-4 + 5) = -7
\]
\[
8x + 1 = -7
\]

### Step 3: Subtract 1 from both sides to isolate the term with \(x\).
\[
8x = -7 - 1
\]
\[
8x = -8
\]

### Step 4: Divide both sides by 8 to solve for \(x\).
\[
x = \frac{-8}{8}
\]
\[
x = -1
\]

So, the solution is \( x = -1 \).

Would you like more details, or do you have any other questions?

Here are 5 related questions to consider:
1. What would be the solution if the equation were \( 4(2x - 3) - 4x + 5 = -7 \)?
2. How would you solve the equation \( 5(2x + 3) - 3x + 4 = 10 \)?
3. What happens if you add 3 to both sides of the equation \( 8x + 1 = -7 \) before solving for \( x \)?
4. Can you solve the equation \( 6x - 2(3x + 4) = 8 \)?
5. How would you approach solving an equation like \( 2x - 5(3x + 2) + 7 = 0 \)?

**Tip:** When solving equations, always ensure that you distribute multiplication correctly across terms within parentheses to avoid mistakes.

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

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