Questions: Solve the inequality. Graph the solution set and write it in interval notation. 5x < -20 Choose the correct graph below. A. B. C. xD. Write the answer in interval notation.

Solve the inequality. Graph the solution set and write it in interval notation.
5x < -20

Choose the correct graph below.
A.
B.
C.
xD.

Write the answer in interval notation.

Transcript text: Solve the inequality. Graph the solution set and write it in interval notation. \[ 5 x<-20 \] Choose the correct graph below. A. B. C. $x_{D}$. Write the answer in interval notation.

Solution

Solution Steps

Step 1: Isolate the variable

To solve the inequality $5x < -20$, we need to isolate $x$. We do this by dividing both sides of the inequality by 5.

\[ \frac{5x}{5} < \frac{-20}{5} \]

Step 2: Simplify the inequality

Simplify the left and right sides of the inequality.

\[ x < -4 \]

Step 3: Graph the solution set

The solution set $x < -4$ is represented on a number line by shading all the numbers to the left of -4 and using an open circle at -4 to indicate that -4 is not included in the solution set.

Step 4: Choose the correct graph

From the given options, the correct graph is the one that shows an open circle at -4 and shading to the left. This corresponds to option A.

Step 5: Write the answer in interval notation

The interval notation for the solution $x < -4$ is $(-\infty, -4)$.