Question

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

-5
-3
-2
-1
1
2
3
O
4
5
+
+
4
-3
-2
-1
0
1
2
4
5
+
w+ W0
+
at at at
+
fr
-3
-2
-1
o
1
2
3
4
5
+
-3
-2
-1
ó
1
2 3
4
5

Answer 1

3 < x

Explanation:

3(8 - 4x) < 6(x - 5)?

Distribute

24 -12x< 6x -30

Add 12x to each side

24-12x+12x < 6x+12x-30

24 < 18x-30

Add 30 to each side

24+30 < 18x-30+30

54 < 18x

Divide each side by 18

54/18 < 18x/18

3 < x