Solve for \( x \): \( -15x = 4000 - 5250 \) which is \( -15x = -1250 \).
["Solve for ( x ) in the Equation: ( -15x = -1250 )", "Understanding how to solve linear equations is a fundamental skill in algebra. One common problem students encounter is isolating the variable to find its value. In this article, we’ll solve the equation:", "[\n-15x = -1250\n]", "and explain how to determine the value of ( x ) step by step.", "---", "### Step 1: Simplify the Right-Hand Side", "Begin by evaluating the constant expression on the right side of the equation:\n[\n-1250\n]\nThis value is already simplified, so the equation remains:\n[\n-15x = -1250\n]", "---", "### Step 2: Isolate the Variable ( x )", "To isolate ( x ), divide both sides of the equation by (-15), the coefficient of ( x ):", "[\nx = \frac{-1250}{-15}\n]", "When dividing two negative numbers, remember that the result is positive:\n[\nx = \frac{1250}{15}\n]", "Now simplify the fraction:", "Divide numerator and denominator by 5:\n[\nx = \frac{250}{3}\n]", "---", "### Step 3: Express the Final Answer", "The solution to the equation is:", "[\nx = \frac{250}{3} \quad \ ext{or approximately} \quad x \approx 83.33\n]", "This means that when multiplied by (-15), ( x ) yields (-1250), satisfying the original equation.", "---", "### Why This Equation Matters", "Solving for ( x ) in equations like this builds critical algebraic reasoning. This particular problem involves negative coefficients and simple arithmetic—common challenges in algebra—and demonstrates how to manipulate both sides of an equation using inverse operations.", "Whether you’re studying algebra, preparing for standardized tests, or brushing up your math skills, mastering this step-by-step process strengthens your foundation for tackling more complex equations.", "---", "### Final Answer:", "[\n\boxed{x = \frac{250}{3}}\n]", "---", "### Bonus Tip: Check Your Work", "Always verify your solution by substituting ( x = \frac{250}{3} ) back into the original equation:\nLeft side:\n[\n-15x = -15 \ imes \frac{250}{3} = -5 \ imes 250 = -1250\n]\nRight side:\n[\n4000 - 5250 = -1250\n]\nBoth sides match, confirming the solution is correct.", "---", "Mastering algebra starts with equations like this—practice makes progress!"]
