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
Fresh day Izatha, let's solve. Here are the solutions for the inequalities in Example 2: Solving the first inequality: 2x - 1 7 Step 1: Add 1 to both sides of the inequality. 2x - 1 + 1 7 + 1 2x 8 Step 2: Divide both sides by 2. (2x)/(2) (8)/(2) x 4 The solution set for this inequality is \x : x 4\. Solving the second inequality: 2x 8x 4 This is a compound inequality, which can be split into two separate inequalities: 1. 2x 8x 2. 8x 4 Step 1: Solve the first part, 2x 8x. Subtract 2x from both sides: 0 8x - 2x 0 6x Divide by 6: (0)/(6) (6x)/(6) 0 x or x 0 Step 2: Solve the second part, 8x 4. Divide by 8: (8x)/(8) (4)/(8) x (1)/(2) Step 3: Combine the solutions for both parts using "AND". We have x 0 and x (1)/(2). Combining these gives: 0 x (1)/(2) The solution set for this inequality is \x : 0 x (1)/(2)\. The "Solution set: \x : x 4\" provided in the image corresponds to the solution of the first inequality, 2x - 1 7. Send me the next one 📸