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

(0.2)(-10.38) + 1,152.882 = (2.5)(x+6.9) - 171.688




We are tasked with solving the following equation for \( x \):

\[
(0.2)(-10.38) + 1,152.882 = (2.5)(x + 6.9) - 171.688
\]

### Step 1: Simplify both sides
First, simplify the left-hand side and the right-hand side.

- Left-hand side:
  \[
  (0.2)(-10.38) = -2.076
  \]
  \[
  -2.076 + 1,152.882 = 1,150.806
  \]

- Right-hand side:
  Distribute \( 2.5 \) on the right-hand side:
  \[
  (2.5)(x + 6.9) = 2.5x + 17.25
  \]
  \[
  2.5x + 17.25 - 171.688 = 2.5x - 154.438
  \]

### Step 2: Set up the simplified equation
Now, the equation becomes:
\[
1,150.806 = 2.5x - 154.438
\]

### Step 3: Solve for \( x \)
Add \( 154.438 \) to both sides:
\[
1,150.806 + 154.438 = 2.5x
\]
\[
1,305.244 = 2.5x
\]

Divide both sides by 2.5 to isolate \( x \):
\[
x = \frac{1,305.244}{2.5}
\]
\[
x = 522.0976
\]

### Final Answer:
\[
x = 522.0976
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would you solve an equation with variables on both sides?
2. What is the process for solving an equation with parentheses and distributive properties?
3. How can you check if your solution is correct in this case?
4. What changes if the equation contains fractions instead of decimals?
5. How do you solve equations involving higher powers of \( x \)?

**Tip:** Always double-check your arithmetic steps to avoid small calculation errors, especially when dealing with decimals.

Solve the following equation for "x". Express your answer as a decimal number with at least four digits past the decimal. (0.2)(-10.38) + 1,152.882 = (2.5)(x+6.9) - 171.688

Learn how to solve a linear equation with decimals: (0.2)(-10.38) + 1,152.882 = (2.5)(x+6.9) - 171.688. This step-by-step guide simplifies the equation, distributes, and solves for x. Suitable for students in Grades 9-10.

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