Final answer:
To illustrate the solution for x ≤ -4 on a number line, shade everything to the left of -4 and include a closed dot at -4, representing all numbers less than or equal to -4.
Step-by-step explanation:
When a student is asked to highlight all of the numbers on each number line for which the statement x ≤ -4 is true, they are working with inequalities in mathematics. To respond to this, the student needs to understand that the statement x ≤ -4 means that x can be any number that is less than or equal to -4. On a number line, this translates to shading all points from -4 to the left indefinitely, denoting all values that are equal to -4 and those that are less than -4.
To sketch the graph, one would draw a thick line or use shading starting from the number -4 and extending towards the left end of the number line to represent all numbers less than or equal to -4. A closed dot is typically used at -4 to indicate that -4 itself is included in the shaded region. This visual representation helps to easily see the group of numbers that satisfy the inequality x ≤ -4.