Question

Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
-5
-4
-3
-2
+
4
-1
0
+
5
1
2
3
-5
-4
-3
-2
-1
+
1
+
2
0
3
4
5
+
-5
-4
-3
-2
-1
+
1
+
2
+
3
+
4
O
5
o
-5
-4
-3
-2
+
1
-1
0
2
2
3
3
4
st
5

Answer 1

Answer:

Option 2 is correct .

Step-by-step explanation:

A inequality is given to us , and we need to find the solution set for it. The given inequality is :-

⇒ 3(8 - 4x) < 6(x - 5)

⇒ 24 - 12x < 6x - 30

⇒ 24 +30 < 6x + 12x

⇒ 54 < 18x

⇒ x > 54/18

⇒ x > 3

This means that x can have all values Greater than 3 . Hence x can have all real numbers greater than 3 . Hence the Solution set will be x ∈ ( 3, ∞ ) . From the number lines given in the option second option is correct .

The solution set is x ∈ ( 3 , ∞ ) .And the second option is correct.

I have also attached the graph . The red area shows the possible values of x.