Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality.
1. To represent all the solutions for the inequality in Part B, a number line would be set up with an open circle on the corresponding value, indicating that the value is not included in the solution. Then, an arrow would be drawn in the direction of the greater values, representing all the numbers larger than the value shown by the open circle.
2. Solving an equation involves finding a value or values that make the equation true. In other words, it aims to determine the specific value(s) that satisfy the equation. On the other hand, solving an inequality involves finding a range or set of values that make the inequality true. In this case, it identifies all the possible value(s) that satisfy the inequality, rather than finding a specific value.
1. To describe the number line set up that would show all of the solutions for an inequality, we need to consider two scenarios: one for a greater than (>) or less than (<) inequality, and another for a greater than or equal to (≥) or less than or equal to (≤) inequality.
For a greater than or less than inequality (e.g., x > 3 or x < -2), the number line would have an open circle at the specific value mentioned in the inequality (3 or -2, respectively), indicating that this value is not included as a solution. Then, an arrow would point in the direction towards positive infinity for a greater than inequality or towards negative infinity for a less than inequality, indicating that all values in that direction are included as solutions.
For a greater than or equal to or less than or equal to inequality (e.g., x ≥ 4 or x ≤ -1), the number line would have a closed circle at the specific value mentioned in the inequality (4 or -1, respectively), indicating that this value is included as a solution. Then, an arrow would point in the direction towards positive infinity for a greater than or equal to inequality or towards negative infinity for a less than or equal to inequality, indicating that all values in that direction are included as solutions.
2. The main difference between solving an equation and solving an inequality lies in the type of solution. When solving an equation, we find the value(s) for the variable that make the equation true. These values are generally specific points or a set of values.
On the other hand, when solving an inequality, we find the range of values that make the inequality true. The solution can be expressed as a range or interval on the number line rather than a single point. Inequalities can have infinitely many solutions, whereas equations typically have a finite number of solutions. The solution to an inequality can include multiple values that satisfy the given conditions, rather than just one specific value as in the case of equations.