Question

solve and graph each solution set. -15≤f(x)<0, where f(x)= -2x - 5. graph the solution. choose the correct graph below.

Explanation:

Step1: Set up the inequalities

We have $-15\leq - 2x - 5<0$. First, solve the left - hand side inequality $-15\leq - 2x - 5$. Add 5 to both sides: $-15 + 5\leq-2x-5 + 5$, which simplifies to $-10\leq - 2x$. Divide both sides by - 2 and reverse the inequality sign (since dividing by a negative number), we get $5\geq x$.

Step2: Solve the right - hand side inequality

Solve $-2x - 5<0$. Add 5 to both sides: $-2x-5 + 5<0 + 5$, which gives $-2x<5$. Divide both sides by - 2 and reverse the inequality sign, we have $x>-\frac{5}{2}$.

Step3: Write the solution set

The solution set is $-\frac{5}{2}-\frac{5}{2}$) and a closed circle at 5 (because $x\leq5$) with a line segment connecting them.

Answer:

The correct graph would have an open circle at $-\frac{5}{2}=-2.5$ and a closed circle at 5 with the line segment between them. Without seeing the exact details of the graphs labeled A - F, the graph that matches this description is the correct one.