La moyenne est donnée par \( \frac{85 + 90 + 95 + x}{4} = 90 \).

["Title: How to Solve for ( x ) in the Equation: ( \frac{85 + 90 + 95 + x}{4} = 90 )", "---", "Understanding the Equation: A Step-by-Step Guide\nSolving equations like ( \frac{85 + 90 + 95 + x}{4} = 90 ) is a common task in algebra and everyday math. This equation helps find the missing number ( x ) that makes the average of four numbers equal to 90. Whether you’re a student learning algebra or someone brushing up on math basics, mastering this process is essential.", "In this article, we’ll break down how to solve for ( x ) using clear steps and real-life context.", "---", "### What Does the Equation Mean?", "The expression ( \frac{85 + 90 + 95 + x}{4} = 90 ) represents the average (mean) of four numbers: 85, 90, 95, and an unknown value ( x ). The average is the sum of all values divided by how many values there are (in this case, 4).", "We’re told the average equals 90, so:", "[\n\frac{85 + 90 + 95 + x}{4} = 90\n]", "---", "### Step 1: Simplify the Known Values", "Before solving for ( x ), add the known numbers in the numerator:", "[\n85 + 90 + 95 = 270\n]", "Now substitute back into the equation:", "[\n\frac{270 + x}{4} = 90\n]", "---", "### Step 2: Eliminate the Denominator", "To simplify, multiply both sides of the equation by 4:", "[\n270 + x = 90 \ imes 4\n]", "[\n270 + x = 360\n]", "---", "### Step 3: Solve for ( x )", "Now isolate ( x ) by subtracting 270 from both sides:", "[\nx = 360 - 270\n]", "[\nx = 90\n]", "---", "### Why This Matters: Real-World Applications", "Average calculations are vital in many fields:\n- Education: To determine a student’s overall grade or class average.\n- Business: To analyze sales, profits, or performance metrics over time.\n- Personal finance: To calculate average monthly expenses or income.", "Knowing how to solve such equations ensures clearer analysis and confident decision-making.", "---", "### Final Answer", "The value of ( x ) that makes the average ( \frac{85 + 90 + 95 + x}{4} = 90 ) is:", "[\n\boxed{90}\n]", "---", "### Summary", "To solve equations of the form ( \frac{\ ext{sum of constants} + x}{n} = \ ext{target average} ):\n1. Compute the sum of known numbers.\n2. Multiply both sides by ( n ) to eliminate the denominator.\n3. Solve algebraically for ( x ).", "Mastering this technique strengthens foundational math skills and supports practical problem-solving daily.", "---", "Keywords: solve for x, average equation, algebra, linear equation, math tutorial, high school algebra, exam preparation, average calculation.", "Meta Description: Learn how to solve ( \frac{85 + 90 + 95 + x}{4} = 90 ) step-by-step — essential algebra for grades 7–12. Perfect for students and educators."]