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The given equation is:

\[ 2(5 - x) + 3(4 - x) = 37 \]

Let’s solve it step-by-step.

### Step 1: Distribute the constants.

\[ 2 \times (5 - x) + 3 \times (4 - x) = 37 \]

This becomes:

\[ 10 - 2x + 12 - 3x = 37 \]

### Step 2: Combine like terms.

\[ (10 + 12) - (2x + 3x) = 37 \]

\[ 22 - 5x = 37 \]

### Step 3: Isolate the variable.

Subtract 22 from both sides:

\[ -5x = 37 - 22 \]

\[ -5x = 15 \]

### Step 4: Solve for \( x \).

Divide both sides by -5:

\[ x = -\frac{15}{5} \]

\[ x = -3 \]

### Solution:

The solution is \( x = -3 \).

Would you like more details or have any questions? 

Here are five related questions:
1. What happens if you change the constants in the equation?
2. How do you solve similar equations with different coefficients?
3. Can this method be applied to equations with fractions?
4. What if the equation had more terms involving \( x \)?
5. How would you graph the original equation?

**Tip:** Always distribute constants carefully when solving linear equations to avoid errors.

Learn how to solve the linear equation 2(5 - x) + 3(4 - x) = 37 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and variable isolation. Suitable for students in Grades 7-9.

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