Solve equations with variables on both sides to find which house Ann lives in.

To determine which house Ann lives in, we need to solve each equation and follow the path based on the solutions. Let's solve each equation step by step.

Step 1: Solve the starting equation

Equation: \( 5x = 3x - 8 \)

1. Subtract \( 3x \) from both sides:
\[
5x - 3x = -8
\]
\[
2x = -8
\]

2. Divide both sides by 2:
\[
x = -4
\]

So, the solution to the starting equation is \( x = -4 \).

Step 2: Follow the path based on the solution

We will now solve each equation along the path until we reach a house.

#### First Equation: \( -4 + x = 5x + 16 \)

1. Subtract \( x \) from both sides:
\[
-4 = 4x + 16
\]

2. Subtract 16 from both sides:
\[
-4 - 16 = 4x
\]
\[
-20 = 4x
\]

3. Divide both sides by 4:
\[
x = -5
\]

So, the solution is \( x = -5 \).

#### Second Equation: \( -5x + 3 = -12 - 2x \)

1. Add \( 2x \) to both sides:
\[
-5x + 2x + 3 = -12
\]
\[
-3x + 3 = -12
\]

2. Subtract 3 from both sides:
\[
-3x = -15
\]

3. Divide both sides by -3:
\[
x = 5
\]

So, the solution is \( x = 5 \).

#### Third Equation: \( -11 + 3x = 4(x + 2) - 27 \)

1. Distribute the 4 on the right side:
\[
-11 + 3x = 4x + 8 - 27
\]
\[
-11 + 3x = 4x - 19
\]

2. Subtract \( 4x \) from both sides:
\[
-11 + 3x - 4x = -19
\]
\[
-11 - x = -19
\]

3. Add 11 to both sides:
\[
-x = -8
\]

4. Multiply both sides by -1:
\[
x = 8
\]

So, the solution is \( x = 8 \).

#### Fourth Equation: \( 4 - 6(x + 2) = 3 - 5x \)

1. Distribute the -6 on the left side:
\[
4 - 6x - 12 = 3 - 5x
\]
\[
-6x - 8 = 3 - 5x
\]

2. Add \( 6x \) to both sides:
\[
-8 = 3 + x
\]

3. Subtract 3 from both sides:
\[
-8 - 3 = x
\]
\[
x = -11
\]

So, the solution is \( x = -11 \).

#### Fifth Equation: \( 5 - 2x + 2 = 4 - x \)

1. Combine like terms on the left side:
\[
7 - 2x = 4 - x
\]

2. Add \( 2x \) to both sides:
\[
7 = 4 + x
\]

3. Subtract 4 from both sides:
\[
7 - 4 = x
\]
\[
x = 3
\]

So, the solution is \( x = 3 \).

#### Sixth Equation: \( -3x - 12 = x - 28 \)

1. Subtract \( x \) from both sides:
\[
-3x - x - 12 = -28
\]
\[
-4x - 12 = -28
\]

2. Add 12 to both sides:
\[
-4x = -16
\]

3. Divide both sides by -4:
\[
x = 4
\]

So, the solution is \( x = 4 \).

#### Seventh Equation: \( 8(6 - x) = -3x + 4 - x \)

1. Distribute the 8 on the left side:
\[
48 - 8x = -3x + 4 - x
\]
\[
48 - 8x = -4x + 4
\]

2. Add \( 8x \) to both sides:
\[
48 = 4x + 4
\]

3. Subtract 4 from both sides:
\[
48 - 4 = 4x
\]
\[
44 = 4x
\]

4. Divide both sides by 4:
\[
x = 11
\]

So, the solution is \( x = 11 \).

#### Eighth Equation: \( 11 + 2x = 3(x + 1) - 2 \)

1. Distribute the 3 on the right side:
\[
11 + 2x = 3x + 3 - 2
\]
\[
11 + 2x = 3x + 1
\]

2. Subtract \( 2x \) from both sides:
\[
11 = x + 1
\]

3. Subtract 1 from both sides:
\[
11 - 1 = x
\]
\[
x = 10
\]

So, the solution is \( x = 10 \).

#### Ninth Equation: \( 7(x + 2) = 2x + 34 \)

1. Distribute the 7 on the left side:
\[
7x + 14 = 2x + 34
\]

2. Subtract \( 2x \) from both sides:
\[
7x - 2x + 14 = 34
\]
\[
5x + 14 = 34
\]

3. Subtract 14 from both sides:
\[
5x = 20
\]

4. Divide both sides by 5:
\[
x = 4
\]

So, the solution is \( x = 4 \).

#### Tenth Equation: \( 3x - 5 + x = 2x + 7 \)

1. Combine like terms on the left side:
\[
4x - 5 = 2x + 7
\]

2. Subtract \( 2x \) from both sides:
\[
4x - 2x - 5 = 7
\]
\[
2x - 5 = 7
\]

3. Add 5 to both sides:
\[
2x = 12
\]

4. Divide both sides by 2:
\[
x = 6
\]

So, the solution is \( x = 6 \).

#### Eleventh Equation: \( 10(4 - x) = 3(x + 5) - 1 \)

1. Distribute the 10 and 3:
\[
40 - 10x = 3x + 15 - 1
\]
\[
40 - 10x = 3x + 14
\]

2. Subtract \( 3x \) from both sides:
\[
40 - 10x - 3x = 14
\]
\[
40 - 13x = 14
\]

3. Subtract 40 from both sides:
\[
-13x = 14 - 40
\]
\[
-13x = -26
\]

4. Divide both sides by -13:
\[
x = 2
\]

So, the solution is \( x = 2 \).

#### Twelfth Equation: \( -10(x - 2) = 5(x + 1) \)

1. Distribute the -10 and 5:
\[
-10x + 20 = 5x + 5
\]

2. Subtract \( 5x \) from both sides:
\[
-10x - 5x + 20 = 5
\]
\[
-15x + 20 = 5
\]

3. Subtract 20 from both sides:
\[
-15x = 5 - 20
\]
\[
-15x = -15
\]

4. Divide both sides by -15:
\[
x = 1
\]

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

#### Thirteenth Equation: \( 6x + 5 = 19 + 3x + 7 \)

1. Combine like terms on the right side:
\[
6x + 5 = 26 + 3x
\]

2. Subtract \( 3x \) from both sides:
\[
6x - 3x + 5 = 26
\]
\[
3x + 5 = 26
\]

3. Subtract 5 from both sides:
\[
3x = 21
\]

4. Divide both sides by 3:
\[
x = 7
\]

So, the solution is \( x = 7 \).

#### Fourteenth Equation: \( -7(x + 5) = -6x + 28 - 2x \)

1. Distribute the -7 on the left side:
\[
-7x - 35 = -6x + 28 - 2x
\]
\[
-7x - 35 = -8x + 28
\]

2. Add \( 8x \) to both sides:
\[
-7x + 8x - 35 = 28
\]
\[
x - 35 = 28
\]

3. Add 35 to both sides:
\[
x = 63
\]

So, the solution is \( x = 63 \).

Final Answer

Following the path based on the solutions, Ann lives in the house corresponding to the final equation solved. The final equation solved is \( -7(x + 5) = -6x + 28 - 2x \), which leads to the house with \( x = 63 \).

\[
\boxed{63}
\]