Let's solve the equation step by step:

Given equation:  
\[ 7(x + 1) + 4 = -2(x - 6) - 10 \]

1. **Distribute the constants** on both sides:

\[
7x + 7(1) + 4 = -2x + 12 - 10
\]

Simplify it:

\[
7x + 7 + 4 = -2x + 2
\]

2. **Combine like terms**:

\[
7x + 11 = -2x + 2
\]

3. **Add \(2x\) to both sides** to get all the \(x\) terms on one side:

\[
7x + 2x + 11 = 2
\]

\[
9x + 11 = 2
\]

4. **Subtract 11** from both sides to isolate the \(x\) term:

\[
9x = 2 - 11
\]

\[
9x = -9
\]

5. **Divide by 9**:

\[
x = \frac{-9}{9} = -1
\]

The solution is \(x = -1\).

Would you like more details on any step? Here are some related problems you can try:

1. Solve for \(x\): \(5(x - 3) + 2 = 3x - 4\)
2. Simplify and solve: \(2(2x + 3) + 7 = 5(x + 1) + 1\)
3. Solve: \(4x + 7 = 2x - 9\)
4. Find \(x\) in the equation: \(6(x + 2) = 3(x - 4)\)
5. Solve: \(10 - 3(x + 2) = 2x - 8\)

**Tip:** Always distribute and combine like terms carefully to avoid mistakes in algebraic manipulation.

Learn how to solve the equation 7(x + 1) + 4 = -2(x - 6) - 10 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, distributive property, and combining like terms. Suitable for students in Grades 7-9.

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