1. **State the problem:** Solve the linear equation $-3.25x + 6.31 = 10.52 + 5.42x$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. This involves combining like terms and using inverse operations such as addition, subtraction, multiplication, and division. 3. **Step-by-step solution:** - Start with the equation: $$-3.25x + 6.31 = 10.52 + 5.42x$$ - Move all $x$ terms to one side by adding $3.25x$ to both sides: $$6.31 = 10.52 + 5.42x + 3.25x$$ - Combine like terms on the right: $$6.31 = 10.52 + 8.67x$$ - Subtract $10.52$ from both sides to isolate the $x$ term: $$6.31 - 10.52 = 8.67x$$ - Simplify the left side: $$-4.21 = 8.67x$$ - Divide both sides by $8.67$ to solve for $x$: $$x = \frac{-4.21}{8.67}$$ - Calculate the division: $$x \approx -0.485$$ 4. **Final answer:** $$x \approx -0.485$$ This means the value of $x$ that satisfies the equation is approximately $-0.485$.