To solve the inequality [tex]\(\frac{a}{-5} \geq 10\)[/tex] step by step, we follow these steps:
1. Rewrite the Inequality: Start with the given inequality.
[tex]$
\frac{a}{-5} \geq 10
$[/tex]
2. Isolate the Variable [tex]\(a\)[/tex]: Multiply both sides of the inequality by [tex]\(-5\)[/tex]. Remember that when multiplying or dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Hence,
[tex]$
a \leq 10 \times (-5)
$[/tex]
3. Simplify the Expression: Compute the right-hand side.
[tex]$
a \leq -50
$[/tex]
Thus, the inequality [tex]\(a \leq -50\)[/tex] explains that [tex]\(a\)[/tex] should be less than or equal to [tex]\(-50\)[/tex].
Graph Representation:
- The correct graph will have a number line.
- There will be a closed circle (•) at [tex]\(a = -50\)[/tex] indicating that [tex]\(-50\)[/tex] is included in the solution.
- The shading (or the arrow indicating the solution set) will extend to the left from [tex]\(-50\)[/tex], showing all numbers less than [tex]\(-50\)[/tex].
In summary, the graph that matches the inequality [tex]\(a \leq -50\)[/tex] will show a closed circle at [tex]\(-50\)[/tex] and shading extending to the left.
