Question

decimals.
0.4y - 2 > 2.4y - 6
part 1 of 3
in set-builder notation, the solution set is {y | y < 2}.
part 2 of 3
in interval notation, the solution set is (-∞, 2).
part: 2 / 3
part 3 of 3
graph the solution set on the number line.
number line image

Explanation:

Step1: Analyze the inequality solution

The solution to the inequality \(0.4y - 2>2.4y - 6\) is \(y < 2\). For graphing on the number line, we need to represent all real numbers less than 2.

Step2: Determine the graph style

Since \(y\) is strictly less than 2 (not including 2), we use an open circle at \(y = 2\) (to indicate that 2 is not included in the solution set) and draw an arrow to the left of 2 (to represent all numbers less than 2).

To graph it:

1. Locate the point 2 on the number line.
2. Draw an open circle at 2 (because the inequality is \(y < 2\), not \(y\leq2\)).
3. Draw a line (or an arrow) starting from the open circle and extending to the left (towards negative infinity) to show all values of \(y\) that satisfy the inequality.

Answer:

To graph the solution set \(y < 2\) on the number line:

• Place an open circle at the point corresponding to \(2\) on the number line (to show that \(2\) is not included in the solution).
• Draw an arrow starting from the open circle and pointing to the left (towards smaller numbers, i.e., negative infinity) to represent all real numbers less than \(2\).