Which of the following describes the graph of {x | x ≤ 1} {x | x ≥ 4}?

closed circles on 1 and 4 with a line segment between
closed circles on 1 and 4 with arrows pointing outward
the entire number line
no solution

  closed circles on 1 and 4 with arrows pointing outward

Step-by-step explanation:

We assume your graph is of ...

  {x | x ≤ 1} ∪ {x | x ≥ 4}

__

The inequality symbols include the "or equal to" case, so the circles at 1 and 4 will be closed.

x ≤ 1 means the arrow points left of x = 1.

x ≥ 4 means the arrow points right of x = 4.

The graph will have arrows pointing outward from the closed circles at x=1 and x=4.

___

If the graph is supposed to be that of

  {x | x ≤ 1} ∩ {x | x ≥ 4}

then there will be no solution. No number can be both left of 1 and right of 4 on the number line.

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.

here's a poem i finished a while ago. i hope you like it and that it inspires you.