how do you write an open statement involving an absolute value inequality when all you are given is the graph of the solution?
To write an open statement involving an absolute value inequality when all you have is the graph of the solution, follow these steps:
Step 1: Identify the x-values for the shaded region
- Locate the boundary vertical lines (or points) on the graph where the shading starts and ends.
- Note the x-coordinate values of those points.
Step 2: Write the absolute value inequality
- Use the x-coordinate values obtained from Step 1 to construct the absolute value inequality.
- Determine whether the inequality is "less than" or "greater than" based on the shading direction.
Step 3: Express the open statement
- Write the inequality in open statement form, which describes the variable and its acceptable values.
- Use inequality symbols (<, >) to represent "less than" or "greater than."
- Include the absolute value sign to represent the magnitude.
For example, suppose the graph shows a shaded region between x = -2 and x = 3. Here's how you can write the open statement:
Step 1: The x-values for the shaded region are -2 and 3.
Step 2: The absolute value inequality is |x| < 3, since the shading falls between -2 and 3.
Step 3: The open statement would be: "The absolute value of x is less than 3."
Remember, when constructing the open statement, reflect the direction of the inequality and ensure the absolute value inequality captures all the points within the shaded region.