Answer :
We start with the inequality
[tex]$$-0.5x \leq 7.5.$$[/tex]
Since the coefficient of [tex]$x$[/tex] is negative, dividing both sides by [tex]$-0.5$[/tex] requires us to flip the direction of the inequality:
[tex]$$
x \geq \frac{7.5}{-0.5}.
$$[/tex]
Calculating the right-hand side:
[tex]$$
\frac{7.5}{-0.5} = -15.
$$[/tex]
Thus, the inequality becomes
[tex]$$
x \geq -15.
$$[/tex]
This means that any number greater than or equal to [tex]$-15$[/tex] satisfies the inequality. On a number line, this is represented by a closed circle at [tex]$-15$[/tex] (indicating that [tex]$-15$[/tex] is included) and shading (or an arrow) to the right, showing that all numbers to the right of [tex]$-15$[/tex] are part of the solution.
Therefore, the graph that correctly shows the solution to the inequality [tex]$-0.5x \leq 7.5$[/tex] is the one with a closed circle at [tex]$-15$[/tex] and shading extending to the right.
[tex]$$-0.5x \leq 7.5.$$[/tex]
Since the coefficient of [tex]$x$[/tex] is negative, dividing both sides by [tex]$-0.5$[/tex] requires us to flip the direction of the inequality:
[tex]$$
x \geq \frac{7.5}{-0.5}.
$$[/tex]
Calculating the right-hand side:
[tex]$$
\frac{7.5}{-0.5} = -15.
$$[/tex]
Thus, the inequality becomes
[tex]$$
x \geq -15.
$$[/tex]
This means that any number greater than or equal to [tex]$-15$[/tex] satisfies the inequality. On a number line, this is represented by a closed circle at [tex]$-15$[/tex] (indicating that [tex]$-15$[/tex] is included) and shading (or an arrow) to the right, showing that all numbers to the right of [tex]$-15$[/tex] are part of the solution.
Therefore, the graph that correctly shows the solution to the inequality [tex]$-0.5x \leq 7.5$[/tex] is the one with a closed circle at [tex]$-15$[/tex] and shading extending to the right.
