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
Welcome back vostaomondi747 — missed you this week. Here are the solutions to the inequalities: 1) Solve -6x + 12 > 0 Step 1: Subtract 12 from both sides. -6x > -12 Step 2: Divide both sides by -6. Remember to reverse the inequality sign when dividing by a negative number. (-6x)/(-6) < (-12)/(-6) x < 2 The solution is x < 2. Graphical Representation: Draw a number line. Place an open circle at 2 (since x is strictly less than 2, 2 is not included). Draw an arrow extending to the left from the open circle, indicating all numbers less than 2. 2) Solve 3(4x - 2) 6 Step 1: Distribute the 3 on the left side. 12x - 6 6 Step 2: Add 6 to both sides. 12x 6 + 6 12x 12 Step 3: Divide both sides by 12. (12x)/(12) (12)/(12) x 1 The solution is x 1. Graphical Representation: Draw a number line. Place a closed circle (or shaded circle) at 1 (since x is greater than or equal to 1, 1 is included). Draw an arrow extending to the right from the closed circle, indicating all numbers greater than or equal to 1. 3) Solve 3 - 4x < 11 Step 1: Subtract 3 from both sides. -4x < 11 - 3 -4x < 8 Step 2: Divide both sides by -4. Remember to reverse the inequality sign when dividing by a negative number. (-4x)/(-4) > (8)/(-4) x > -2 The solution is x > -2. Graphical Representation: Draw a number line. Place an open circle at -2 (since x is strictly greater than -2, -2 is not included). Draw an arrow extending to the right from the open circle, indicating all numbers greater than -2. Send me the next one 📸