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
You're on a roll — here are the number line representations for the remaining parts of Question 2: Question 2: Indicate the region of the number line that represents the following. B) x -2 OR x < -4 Step 1: Understand the first inequality, x -2. This means x is less than or equal to -2. On a number line, this is represented by a solid dot at -2 and shading to the left. Step 2: Understand the second inequality, x < -4. This means x is less than -4. On a number line, this is represented by an open dot at -4 and shading to the left. Step 3: Combine the inequalities using "OR". The "OR" condition means that x must satisfy at least one of the inequalities. Since all numbers less than or equal to -2 also include numbers less than -4, the combined region is x -2. Number line representation: Draw a number line. Place a solid dot (•) at -2. Shade the region to the left of -2. <---•---------------------> -2 C) x 2 OR x 6 Step 1: Understand the first inequality, x 2. This means x is less than or equal to 2. On a number line, this is represented by a solid dot at 2 and shading to the left. Step 2: Understand the second inequality, x 6. This means x is greater than or equal to 6. On a number line, this is represented by a solid dot at 6 and shading to the right. Step 3: Combine the inequalities using "OR". The "OR" condition means that x must satisfy at least one of the inequalities. These are two separate regions. Number line representation: Draw a number line. Place a solid dot (•) at 2 and shade to the left. Place a solid dot (•) at 6 and shade to the right. <---•--------------------•---> 2 6 D) x < -2 AND x -7 Step 1: Understand the first inequality, x < -2. This means x is less than -2. On a number line, this is represented by an open dot at -2 and shading to the left. Step 2: Understand the second inequality, x -7. This means x is greater than or equal to -7. On a number line, this is represented by a solid dot at -7 and shading to the right. Step 3: Combine the inequalities using "AND". The "AND" condition means that x must satisfy both inequalities simultaneously. The region where both are true is between -7 (inclusive) and -2 (exclusive). Number line representation: Draw a number line. Place a solid dot (•) at -7. Place an open dot (○) at -2. Shade the region between -7 and -2. <---•------------------○---> -7 -2 E) x 0 OR x -6 Step 1: Understand the first inequality, x 0. This means x is greater than or equal to 0. On a number line, this is represented by a solid dot at 0 and shading to the right. Step 2: Understand the second inequality, x -6. This means x is less than or equal to -6. On a number line, this is represented by a solid dot at -6 and shading to the left. Step 3: Combine the inequalities using "OR". The "OR" condition means that x must satisfy at least one of the inequalities. These are two separate regions. Number line representation: Draw a number line. Place a solid dot (•) at -6 and shade to the left. Place a solid dot (•) at 0 and shade to the right. <---•--------------------•---> -6 0 What's next?