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
Here are the solutions to questions 4 and 5. Question 4: Factorize completely (h^2 - k^2) - p(h + k) Step 1: Factor the difference of squares term. The expression h^2 - k^2 is a difference of squares, which factors as (h - k)(h + k). Step 2: Substitute the factored term back into the expression. (h - k)(h + k) - p(h + k) Step 3: Factor out the common term (h + k). (h + k)[(h - k) - p] Step 4: Simplify the expression inside the brackets. (h + k)(h - k - p) The correct option is D. Question 5: Solve 2x - 3 4x + 5 < 3x + 7. This compound inequality can be split into two separate inequalities: 1. 2x - 3 4x + 5 2. 4x + 5 < 3x + 7 Step 1: Solve the first inequality, 2x - 3 4x + 5. Subtract 2x from both sides: -3 2x + 5 Subtract 5 from both sides: -3 - 5 2x -8 2x Divide by 2: (-8)/(2) x -4 x Step 2: Solve the second inequality, 4x + 5 < 3x + 7. Subtract 3x from both sides: x + 5 < 7 Subtract 5 from both sides: x < 7 - 5 x < 2 Step 3: Combine the solutions from Step 1 and Step 2. We have x -4 and x < 2. Combining these gives: -4 x < 2 The correct option is D. That's 2 down. 3 left today — send the next one.