Question

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

O
O
-5 -
-5
&
.4
T
-3
- -3
T
3 op.
?
Y
-2
-1 0 1 2 3
-1 0 1
-1 0 1
-1 0 1
2
2
2
3 4 5
3
4 5
3
4
14
5
10
5

Answer 1

Explanation:

The correct number line to represent the solution set for the inequality 3(8-4x) < 6(x-5) is:

-3 -2 -1 0 1 2 3

To find the solution set, we need to simplify the inequality. Let's start by distributing the 3 on the left side and the 6 on the right side:

24 - 12x < 6x - 30

Next, let's combine like terms:

36 < 18x

Now, let's divide both sides of the inequality by 18 to isolate x:

36/18 < x

2 < x

This means that x is greater than 2. So, the solution set is all the numbers greater than 2.

On the number line, we represent this by starting at 2 and extending the line to the right. So the number line representing the solution set is:

-3 -2 -1 0 1 2 3