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 for the given inequalities, including their representation. 1) Solve 3x < 6: Step 1: Divide both sides by 3. (3x)/(3) < (6)/(3) x < 2 The solution is x < 2. To represent this solution on a number line, draw a number line. Place an open circle at 2 (because x is strictly less than 2, not equal to 2). Then, draw a line extending from the open circle to the left, indicating all numbers less than 2. 2) Solve -2x - 1 ≥ 5: Step 1: Add 1 to both sides of the inequality. -2x - 1 + 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. To represent this solution on a number line, draw a number line. Place a closed circle (or a filled dot) at -3 (because x is less than or equal to -3). Then, draw a line extending from the closed circle to the left, indicating all numbers less than or equal to -3. That's 2 down. 3 left today — send the next one.