Whenever you multiply or divide across an inequality by a negative number, you change the direction.
Think about 2 > -4
Multiply both sides by a -3
-6 > 12 NO... change the inequality -6<12
When you are solving inequalities, when does the sign change and when does it not?
For example, in -4x -5 > 8
I know I add 5 to both sides, then I have -4x > 13
Divide both sides by -4 and it becomes x < -3.25
But WHY does the direction of the sign change?
In 9x + 6 > 7, I subtract 6 from both sides to get 9x > 1
Divide both sides by 9 and I get x > 1/9, so the sign stays the same.
Could someone please explain for me?
2 answers
the "direction change" rule is just a shortcut for when things move from one side of the inequality to the other. When adding and subtracting, or multiplying/dividing by a positive value, the direction never changes.
-4x < 8
divide by -4 and change direction:
x > -2
OR
-4x < 8
0 < 8 + 4x
-8 < 4x
-2 < x
they both end up the same
-4x < 8
divide by -4 and change direction:
x > -2
OR
-4x < 8
0 < 8 + 4x
-8 < 4x
-2 < x
they both end up the same