https://file.aiquickdraw.com/mathbot/file/1726644838815vhao2v5t.jpg

The image contains the following equations:

1. \( p = x + 32 \)
2. \( q = x + 40 \)
3. \( 180 = m + 40 + p \)
4. \( 180 = m + q + 32 \)

You are asked to solve for \( x \).

### Step-by-step solution:

1. From equation (1), \( p = x + 32 \).
2. From equation (2), \( q = x + 40 \).

Substitute these values of \( p \) and \( q \) into equations (3) and (4):

#### Substituting into equation (3):
\[
180 = m + 40 + (x + 32)
\]
Simplify:
\[
180 = m + 40 + x + 32
\]
\[
180 = m + x + 72
\]
\[
m + x = 108 \quad \text{(Equation 5)}
\]

#### Substituting into equation (4):
\[
180 = m + (x + 40) + 32
\]
Simplify:
\[
180 = m + x + 40 + 32
\]
\[
180 = m + x + 72
\]
\[
m + x = 108 \quad \text{(Equation 6)}
\]

Since both equations (5) and (6) give the same result, \( m + x = 108 \).

This doesn't provide additional information to directly solve for \( x \), but these constraints can be used to solve for \( m \) if needed.

Do you have any specific variables or values you would like me to solve further or clarify?

### Follow-up questions:
1. Would you like to solve for \( m \) or any other variable?
2. Can you confirm if any specific values for \( m \), \( p \), or \( q \) are given elsewhere?
3. Would you like a further breakdown of steps for a clearer explanation?
4. Are these equations related to any specific geometric or algebraic problem?
5. Would you like help graphing or visualizing the solutions?

#### Tip: Always check if there are specific known values or constraints for variables like \( m \) to simplify solutions.

Solve for x given the following equations: 1) p = x + 32, 2) q = x + 40, 3) 180 = m + 40 + p, 4) 180 = m + q + 32.

Learn how to solve for x in a system of linear equations involving p, q, and m. The problem covers essential algebraic concepts and provides a step-by-step guide to substitution and simplification.

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