To determine which inequality has an arrow pointing to the left when graphed on a number line, we need to understand what each type of inequality represents in terms of direction on the number line.
1. [tex]$x \leq 5$[/tex]:
- The inequality [tex]$x \leq 5$[/tex] means all values of [tex]$x$[/tex] that are less than or equal to 5.
- When graphed on a number line, this corresponds to shading all numbers to the left of 5, including 5 itself.
- This would typically be represented by a closed circle at 5 and an arrow extending to the left.
2. [tex]$4 \leq x$[/tex]:
- This inequality can also be written as [tex]$x \geq 4$[/tex].
- It means all values of [tex]$x$[/tex] that are greater than or equal to 4.
- When graphed, it involves shading all numbers to the right of 4, including 4 itself, with a closed circle at 4 and an arrow extending to the right.
3. [tex]$x \geq -8$[/tex]:
- This represents all values of [tex]$x$[/tex] that are greater than or equal to -8.
- On the number line, it would be shaded from -8 to the right, including -8.
- A closed circle would be at -8, and the arrow would extend to the right.
4. [tex]$x > 6$[/tex]:
- This inequality means all values of [tex]$x$[/tex] strictly greater than 6.
- It would be graphed with an open circle at 6 and shading to the right of this point, as 6 itself is not included.
- An arrow would extend to the right from the open circle at 6.
Based on these explanations, the inequality that has an arrow pointing to the left when the solution set is graphed on a number line is:
[tex]\[ x \leq 5 \][/tex]
Therefore, the correct inequality is:
[tex]\[ x \leq 5 \][/tex]
