Problem: -2(x+4)+6x < 8
can you show me the correct answer to this problem because i do not understand it.
Follow the same steps you would use to solve an equation.
-2(x + 4) + 6x < 8
-2x - 8 + 6x < 8
4x - 8 < 8
4x - 8 + 8 < 8 + 8
4x < 16
4x/4 < 16/4
x < 4
If you use 4 or anything larger, the inequality
is false.
-2(x + 4) + 6x < 8
-2(4 + 4) + 6(4) < 8
-2(8) + 24 < 8
-16 + 24 < 8
8 < 8
It doesn't work, because 8 is NOT less than 8.
-2(x + 4) + 6x < 8
-2(5 + 4) + 6(5) < 8
-2(9) + 30 < 8
-18 + 30 < 8
12 < 8
Again, it doesn't work, because 12 is NOT less than 8.
Use a number that IS smaller than 4.
-2(x + 4) + 6x < 8
-2(3.5 + 4) + 6(3.5) < 8
-2(7.5) + 21 < 8
-15 + 21 < 8
6 < 8
This works, because 6 IS less than 8. It will continue
to work for ANY value of x that is less than 4.