Question

name:
graph the inequality on a number line.
① ( m leq 1 ) ② ( w > 6 )

Explanation:

For \( m \leq 1 \):

Step 1: Understand the inequality

The inequality \( m \leq 1 \) means all real numbers \( m \) that are less than or equal to 1.

Step 2: Mark the point on the number line

Locate the number 1 on the number line. Since the inequality is "less than or equal to", we use a closed (filled - in) circle at 1 to indicate that 1 is included in the solution set.

Step 3: Draw the arrow

Draw an arrow to the left of 1 (towards negative infinity) to show that all numbers less than 1 are also part of the solution set.

For \( w > 6 \):

Step 1: Understand the inequality

The inequality \( w > 6 \) means all real numbers \( w \) that are greater than 6.

Step 2: Mark the point on the number line

Locate the number 6 on the number line. Since the inequality is "greater than" (not "greater than or equal to"), we use an open (not filled - in) circle at 6 to indicate that 6 is not included in the solution set.

Step 3: Draw the arrow

Draw an arrow to the right of 6 (towards positive infinity) to show that all numbers greater than 6 are part of the solution set.

Graphical Representation Summary:

• For \( m \leq 1 \): Closed circle at 1, arrow to the left.
• For \( w > 6 \): Open circle at 6, arrow to the right.

Answer:

Step 1: Understand the inequality

The inequality \( w > 6 \) means all real numbers \( w \) that are greater than 6.

Step 2: Mark the point on the number line

Locate the number 6 on the number line. Since the inequality is "greater than" (not "greater than or equal to"), we use an open (not filled - in) circle at 6 to indicate that 6 is not included in the solution set.

Step 3: Draw the arrow

Draw an arrow to the right of 6 (towards positive infinity) to show that all numbers greater than 6 are part of the solution set.

Graphical Representation Summary:

• For \( m \leq 1 \): Closed circle at 1, arrow to the left.
• For \( w > 6 \): Open circle at 6, arrow to the right.