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 the inequalities: 1. 4x + 2 > -6 Step 1: Subtract 2 from both sides of the inequality. 4x + 2 - 2 > -6 - 2 4x > -8 Step 2: Divide both sides by 4. (4x)/(4) > (-8)/(4) x > -2 The solution is x > -2. 2. 1 - 2x -5 Step 1: Subtract 1 from both sides of the inequality. 1 - 2x - 1 -5 - 1 -2x -6 Step 2: Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number. (-2x)/(-2) (-6)/(-2) x 3 The solution is x 3. 3. (3x+2)/(4) 2 Step 1: Multiply both sides by 4. (3x+2)/(4) × 4 2 × 4 3x + 2 8 Step 2: Subtract 2 from both sides. 3x + 2 - 2 8 - 2 3x 6 Step 3: Divide both sides by 3. (3x)/(3) (6)/(3) x 2 The solution is x 2. 4. (3-2x)/(2) > -3 Step 1: Multiply both sides by 2. (3-2x)/(2) × 2 > -3 × 2 3 - 2x > -6 Step 2: Subtract 3 from both sides. 3 - 2x - 3 > -6 - 3 -2x > -9 Step 3: Divide both sides by -2. Remember to reverse the inequality sign. (-2x)/(-2) < (-9)/(-2) x < (9)/(2) The solution is x < (9)/(2). 5. (1)/(2)(x+4) < 3 Step 1: Multiply both sides by 2. (1)/(2)(x+4) × 2 < 3 × 2 x + 4 < 6 Step 2: Subtract 4 from both sides. x + 4 - 4 < 6 - 4 x < 2 The solution is x < 2. 6. 3(1-2x) 5 Step 1: Distribute the 3 on the left side. 3 × 1 - 3 × 2x 5 3 - 6x 5 Step 2: Subtract 3 from both sides. 3 - 6x - 3 5 - 3 -6x 2 Step 3: Divide both sides by -6. Remember to reverse the inequality sign. (-6x)/(-6) (2)/(-6) x -(1)/(3) The solution is x -(1)/(3). Send me the next one 📸