1. The problem asks to solve the equation by graphing both sides: $$ (2x - 7)(x + 2) = (3 - x)(1 + 4x) $$ 2. First, expand both sides to get explicit functions: Left side: $$ (2x - 7)(x + 2) = 2x \cdot x + 2x \cdot 2 - 7 \cdot x - 7 \cdot 2 = 2x^2 + 4x - 7x - 14 = 2x^2 - 3x - 14 $$ Right side: $$ (3 - x)(1 + 4x) = 3 \cdot 1 + 3 \cdot 4x - x \cdot 1 - x \cdot 4x = 3 + 12x - x - 4x^2 = -4x^2 + 11x + 3 $$ 3. Define two functions: $$ f(x) = 2x^2 - 3x - 14 $$ $$ g(x) = -4x^2 + 11x + 3 $$ 4. To solve the equation graphically, enter these two functions into your calculator or graphing software. 5. On your calculator, type: For $f(x)$: 2x^2 - 3x - 14 For $g(x)$: -4x^2 + 11x + 3 6. Graph both functions on the same coordinate plane. 7. The solutions to the equation are the x-values where the graphs intersect. 8. Use the calculator's intersection feature to find these points. 9. The x-coordinates of the intersection points are the solutions to the original equation. This method visually shows where the two expressions are equal.