\[ y = 2\left(-\frac{4}{5}\right) + 3 = -\frac{8}{5} + \frac{15}{5} = \frac{7}{5} \]

["# Simplifying a Linear Equation: A Step-by-Step Tutorial on ( y = 2\left(-\frac{4}{5}\right) + 3 = -\frac{8}{5} + \frac{15}{5} = \frac{7}{5} )", "Understanding how to simplify and solve linear equations is a fundamental skill in algebra. In this article, we’ll break down the expression ( y = 2\left(-\frac{4}{5}\right) + 3 ) step by step to arrive at the simplified form ( y = \frac{7}{5} ). Whether you're a student practicing math or someone brushing up on core algebra, this guide will clarify the process behind evaluating and simplifying rational expressions in equations.", "### Step 1: Evaluate the Multiplication Inside the Parentheses", "Start with the expression:", "[\ny = 2\left(-\frac{4}{5}\right) + 3\n]", "Here, the number ( 2 ) is being multiplied by ( -\frac{4}{5} ). Multiplying a whole number by a fraction is straightforward:", "[\n2 \ imes \left(-\frac{4}{5}\right) = 2 \cdot \left(-\frac{4}{5}\right) = -\frac{8}{5}\n]", "This step transforms the original equation into:", "[\ny = -\frac{8}{5} + 3\n]", "### Step 2: Convert Whole Number to a Fraction", "To add fractions and whole numbers, both terms must have the same denominator. The fraction here is ( 3 ), which can be written as ( \frac{3}{1} ). To convert it:", "[\n3 = \frac{3 \ imes 5}{1 \ imes 5} = \frac{15}{5}\n]", "Now substitute back into the equation:", "[\ny = -\frac{8}{5} + \frac{15}{5}\n]", "### Step 3: Perform the Addition of Fractions", "With common denominators, subtract the numerators:", "[\n-\frac{8}{5} + \frac{15}{5} = \frac{-8 + 15}{5} = \frac{7}{5}\n]", "Thus, the final simplified expression is:", "[\ny = \frac{7}{5}\n]", "### Why Simplifying Linear Equations Matters", "Simplifying expressions like this is crucial because it helps solve equations efficiently, understand relationships in graphs, and apply algebraic techniques in real-world problems. Mastering how to combine integers and fractions within linear equations builds a solid foundation for advanced mathematics, including calculus and algebra II.", "### Conclusion", "From multiplication and common denominators to direct addition, simplifying ( y = 2\left(-\frac{4}{5}\right) + 3 ) demonstrates a clear step-by-step approach:", "[\n2\left(-\frac{4}{5}\right) + 3 = -\frac{8}{5} + \frac{15}{5} = \frac{7}{5}\n]", "Learn these steps to improve your algebraic fluency and tackle more complex equations with confidence. Keep practicing, and remember: algebra techniques empower you to solve problems logically and precisely!", "---", "Keywords: linear equations, simplifying expressions, algebraic operations, rational numbers, fraction addition, solving for y, step-by-step math tutorial, algebra basics, math simplification tips, evaluating expressions."]