This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve for y in the determinant equation. The determinant of a 2 × 2 matrix a & b \\ c & d is given by ad - bc. Given the equation y-1 & 2 \\ 4 & 3 = -4, we set up the determinant: (y-1)(3) - (2)(4) = -4 3y - 3 - 8 = -4 3y - 11 = -4 Step 2: Isolate y. Add 11 to both sides of the equation: 3y = -4 + 11 3y = 7 Divide by 3: y = (7)/(3) The value of y is (7)/(3). Step 3: Solve the first inequality for x. Given the inequality 2x+5 1: 2x 1 - 5 2x -4 x (-4)/(2) x -2 Step 4: Solve the second inequality for x. Given the inequality (x)/(3) < 4: x < 4 × 3 x < 12 Step 5: Combine the solutions to find the interval for x. We need x to satisfy both x -2 and x < 12. This means x is greater than or equal to -2 and less than 12. The interval is expressed as: [-2, 12) The interval in which x must be is [-2, 12). Send me the next one 📸