Solve the inequality and graph the solution on the line provided.

Question

3, x, minus, 8, is less than, minus, 20
3x−8<
−20

Answer 1

Let's solve the inequality \(3x - 8 < -20\).

1. Start by adding 8 to both sides of the inequality: \[ 3x - 8 + 8 < -20 + 8 \] This simplifies to: \[ 3x < -12 \]

2. Next, divide both sides by 3: \[ x < -4 \]

So, the solution to the inequality is: \[ x < -4 \]

Now, we can graph the solution on a number line:

1. Draw a horizontal line to represent the number line.
2. Identify the point \(-4\) on the line.
3. Since \(x\) can be any number less than \(-4\), draw an open circle at \(-4\) (indicating that \(-4\) is not included in the solution).
4. Shade the line to the left of \(-4\) to show that all numbers less than \(-4\) are included in the solution.

Here's a representation of how the number line would look:

<---|----|----|----|----|----|----|----|----|----|---->
    -6   -5   -4   -3   -2   -1   0    1    2    3

          o
<==========

The open circle at \(-4\) indicates that \(-4\) is not part of the solution, and the shaded area to the left indicates all values less than \(-4\) are included in the solution.