Which graph represents the inequality 2.5 is less than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
The correct graph representation would be: number line with open circle on point negative 5 and arrow shaded to the right.
The graph that represents the inequality "2.5 is less than the product of -0.5 and a number" is the number line with an open circle on the point -5 and an arrow shaded to the right.
To find the graph representing the inequality, we need to analyze the given condition: "2.5 is less than the product of -0.5 and a number."
To start, let's translate the given condition into an inequality:
2.5 < -0.5x
Now, we can simplify the inequality by dividing both sides by -0.5, but we need to remember that when we divide or multiply by a negative number, we need to flip the inequality sign:
2.5 ÷ -0.5 > x
-5 > x
The simplified inequality is -5 > x, which means "x is less than -5".
Now, let's analyze the answer choices to match the inequality -5 > x:
1. number line with open circle on point 0.2 and arrow shaded to the left:
0.2 is greater than -5, so this is not the correct graph.
2. number line with open circle on point -5 and arrow shaded to the left:
This correctly represents the inequality. It shows an open circle at -5 (meaning -5 is not included), and the shaded arrow extends to the left.
3. number line with open circle on point -0.2 and arrow shaded to the right:
This does not represent the inequality correctly. It is opposite to the intended direction.
4. number line with open circle on point -5 and arrow shaded to the right:
This does not represent the inequality correctly. Again, it is opposite to the intended direction.
Therefore, the correct graph representing the inequality 2.5 is less than the product of -0.5 and a number is option 2: a number line with an open circle on -5 and an arrow shaded to the left.