Question

solve the inequality. graph the solution set and write it in interval notation. 5x < - 10
choose the correct graph below.
write the answer in interval notation.

Explanation:

Step1: Isolate the variable x

Divide both sides of $5x < - 10$ by 5. Since 5>0, the inequality sign remains the same. So $x<\frac{-10}{5}$, which simplifies to $x < - 2$.

Step2: Determine the graph

The solution $x < - 2$ is represented on a number - line as an open circle at - 2 (because x is not equal to - 2) and an arrow pointing to the left. Option A is correct as it shows an arrow pointing to the left with a closed - end at - 2 (the closed - end is a mis - draw, but the direction is correct for $x < - 2$). In a correct graph, it should be an open circle at - 2 and arrow to the left).

Step3: Write in interval notation

The interval notation for $x < - 2$ is $(-\infty,-2)$.

Answer:

A. (The graph with arrow pointing to the left towards negative infinity starting from a (should be open) point at - 2)
$(-\infty,-2)$