Solve the following equation for "n". Express your answer as a decimal number with **at least four digits past the decimal.**

30.64 = (29.277)(x) + (30.908)(0.656-x) + 30.558




The given equation is:

\[
30.64 = 29.277x + 30.908(0.656 - x) + 30.558
\]

Let’s first distribute and simplify the equation.

### Step 1: Expand the expression
\[
30.908(0.656 - x) = 30.908 \times 0.656 - 30.908x
\]
\[
30.908 \times 0.656 = 20.270848
\]
Thus, the equation becomes:
\[
30.64 = 29.277x + 20.270848 - 30.908x + 30.558
\]

### Step 2: Combine constants
\[
30.64 = (29.277x - 30.908x) + (20.270848 + 30.558)
\]
\[
30.64 = -1.631x + 50.828848
\]

### Step 3: Isolate the term with \(x\)
\[
30.64 - 50.828848 = -1.631x
\]
\[
-20.188848 = -1.631x
\]

### Step 4: Solve for \(x\)
\[
x = \frac{-20.188848}{-1.631}
\]
\[
x \approx 12.379417
\]

Thus, the solution is \(x \approx 12.3794\).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How can we verify the solution by substituting the value of \(x\) back into the original equation?
2. What happens if one of the constants in the equation changes?
3. Can you solve a similar equation using fractions instead of decimals?
4. How would the equation change if the term with \(x\) was squared?
5. How does this approach generalize to solving more complex linear equations?

**Tip:** When solving for a variable, ensure all like terms are combined before isolating the variable for accuracy.

Solve the following equation for 'n'. Express your answer as a decimal number with at least four digits past the decimal.

30.64 = (29.277)(x) + (30.908)(0.656 - x) + 30.558

Learn how to solve the linear equation 30.64 = (29.277)(x) + (30.908)(0.656 - x) + 30.558 using step-by-step simplification and algebraic methods. This problem demonstrates the distributive property and combining like terms to isolate the variable. Suitable for Grades 9-10.

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