Question

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

Answer 1

Answer: Option B

Explanation:

Answer 2

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Explanation:

We can start by dividing the inequality by 3 to get ...

8 -4x < 2(x -5)

And we can divide by 2 to simplify further to ...

4 -2x < x -5

Now, we can add 2x+5, which gives ...

9 < 3x

and then divide by 3 again:

3 < x

This is graphed on a number line as described above.