Solving Two-Step Equations Maze Activity by The Unique Expressions - Free Printable

To solve the problem, we need to work through each equation step by step and follow the path from "START" to "FINISH." Each equation will lead us to a specific number, which corresponds to the next equation in the sequence. Let's go through this systematically.

Step 1: Start with the first equation

The starting equation is:
\[ -50 + 60 + 4x = 2 \]

Solve for \( x \):
\[
-50 + 60 + 4x = 2 \\
10 + 4x = 2 \\
4x = 2 - 10 \\
4x = -8 \\
x = \frac{-8}{4} \\
x = -2
\]

So, the solution to the first equation is \( x = -2 \). This corresponds to the number -2 in the grid.

Step 2: Move to the next equation

Following the path, the next equation is:
\[ -6 + 5 + 5x = 5 \]

Solve for \( x \):
\[
-6 + 5 + 5x = 5 \\
-1 + 5x = 5 \\
5x = 5 + 1 \\
5x = 6 \\
x = \frac{6}{5}
\]

So, the solution to this equation is \( x = \frac{6}{5} \). This corresponds to the number 5 in the grid.

Step 3: Continue solving equations

We continue this process for each equation, following the path indicated by the solutions. Let's summarize the steps for each equation:

#### Equation 2:
\[ 100 + 5x - 9 = 31 \]
\[
100 + 5x - 9 = 31 \\
91 + 5x = 31 \\
5x = 31 - 91 \\
5x = -60 \\
x = \frac{-60}{5} \\
x = -12
\]
Solution: \( x = -12 \) (corresponds to -12)

#### Equation 3:
\[ -52 + 8x + 1 = -3 \]
\[
-52 + 8x + 1 = -3 \\
-51 + 8x = -3 \\
8x = -3 + 51 \\
8x = 48 \\
x = \frac{48}{8} \\
x = 6
\]
Solution: \( x = 6 \) (corresponds to 6)

#### Equation 4:
\[ -36 + 8 - 9x = 15 \]
\[
-36 + 8 - 9x = 15 \\
-28 - 9x = 15 \\
-9x = 15 + 28 \\
-9x = 43 \\
x = \frac{-43}{9}
\]
Solution: \( x = \frac{-43}{9} \) (corresponds to 15)

#### Equation 5:
\[ -60 + 28 + 4x = 22 \]
\[
-60 + 28 + 4x = 22 \\
-32 + 4x = 22 \\
4x = 22 + 32 \\
4x = 54 \\
x = \frac{54}{4} \\
x = \frac{27}{2}
\]
Solution: \( x = \frac{27}{2} \) (corresponds to 22)

#### Equation 6:
\[ -8 + 18 + 6x = 2.3 \]
\[
-8 + 18 + 6x = 2.3 \\
10 + 6x = 2.3 \\
6x = 2.3 - 10 \\
6x = -7.7 \\
x = \frac{-7.7}{6} \\
x = -1.2833
\]
Solution: \( x = -1.2833 \) (corresponds to 2.3)

#### Equation 7:
\[ 6 + 1 + 2x = 17 \]
\[
6 + 1 + 2x = 17 \\
7 + 2x = 17 \\
2x = 17 - 7 \\
2x = 10 \\
x = \frac{10}{2} \\
x = 5
\]
Solution: \( x = 5 \) (corresponds to 17)

#### Equation 8:
\[ -90 - 10x + 200 = -1 \]
\[
-90 - 10x + 200 = -1 \\
110 - 10x = -1 \\
-10x = -1 - 110 \\
-10x = -111 \\
x = \frac{-111}{-10} \\
x = 11.1
\]
Solution: \( x = 11.1 \) (corresponds to -1)

#### Equation 9:
\[ -6 + 7x + 4 = 6 \]
\[
-6 + 7x + 4 = 6 \\
-2 + 7x = 6 \\
7x = 6 + 2 \\
7x = 8 \\
x = \frac{8}{7}
\]
Solution: \( x = \frac{8}{7} \) (corresponds to 6)

#### Equation 10:
\[ -6 - 5 + 5x = 3 \]
\[
-6 - 5 + 5x = 3 \\
-11 + 5x = 3 \\
5x = 3 + 11 \\
5x = 14 \\
x = \frac{14}{5}
\]
Solution: \( x = \frac{14}{5} \) (corresponds to 3)

Final Answer:

After solving all the equations and following the path, we reach the "FINISH" point. The final answer is:
\[
\boxed{3}
\]