y - 2 = -\frac{3}{4} \left(3 - \frac{3}{2} \right) = -\frac{3}{4} \cdot \frac{3}{2} = -\frac{9}{8}

["# Solving the Equation: ( y - 2 = -\frac{3}{4} \left(3 - \frac{3}{2} \right) = -\frac{9}{8} )", "Understanding how to translate mathematical expressions into clear, step-by-step solutions is essential for students, educators, and math enthusiasts alike. One commonly encountered problem involves solving a linear equation that combines subtraction and multiplication with fractions. In this article, we'll break down the process of solving the equation:", "[\ny - 2 = -\frac{3}{4} \left(3 - \frac{3}{2} \right) = -\frac{9}{8}\n]", "## Breaking Down the Equation Step-by-Step", "### Step 1: Simplify inside the Parentheses", "Start by simplifying the expression inside the parentheses:", "[\n3 - \frac{3}{2} = \frac{6}{2} - \frac{3}{2} = \frac{3}{2}\n]", "### Step 2: Multiply by (-\frac{3}{4})", "Now substitute back and multiply:", "[\n-\frac{3}{4} \left(\frac{3}{2}\right) = -\frac{9}{8}\n]", "This confirms the expression simplifies correctly.", "### Step 3: Rewrite the Original Equation", "Putting it all together:", "[\ny - 2 = -\frac{9}{8}\n]", "### Step 4: Solve for ( y )", "Add 2 to both sides to isolate ( y ):", "[\ny = -\frac{9}{8} + 2\n]", "Convert 2 into a fraction with denominator 8:", "[\n2 = \frac{16}{8}\n]", "So:", "[\ny = -\frac{9}{8} + \frac{16}{8} = \frac{7}{8}\n]", "## Final Answer", "[\ny = \frac{7}{8}\n]", "## Why This Equation Matters", "This problem illustrates key algebraic skills: simplifying expressions with fractions, distributing signs in multiplication, and isolating variables. Mastery of such steps builds a strong foundation for more complex equations and algebraic reasoning.", "## Practice Problem", "Try solving for ( y ) in:", "[\ny + \frac{1}{3} = -\frac{3}{5} \left(6 - \frac{1}{2} \right)\n]", "Use the same method to simplify, multiply, and isolate ( y ).", "## Conclusion", "Equation-solving like ( y - 2 = -\frac{3}{4} \left(3 - \frac{3}{2} \right) ) is more than arithmetic—it builds logical thinking and fluency with fractions and operations. Keep practicing, and gradually, algebraic expressions will become second nature.", "---", "Keywords:\ny - 2 = -3/4 (3 - 3/2), solving linear equation, algebra basics, fraction multiplication, solving equations step-by-step, equation simplification, y = 7/8, algebra tutorial"]