Notation:
< - Less Than...
> - More Than... |
≤ - Less Than or Equal to...
≥ - More Than or Equal to... |
WHEN YOU MULTIPLY OR DIVIDE AN EQUALITY BY A NEGATIVE NUMBER, YOU MUST FLIP OR REVERSE THE INEQUALITY SIGN.
Basic Linear Inequalities:
12-3x < 27 (+3x)
12 < 3x+27 (-27) -15 < 3x (/3) -5 < x |
3(x-5) > 5-2(x-8) (expand)
3x-15 > 5-2x+16 3x-15 > -2x+21 (+2x) 5x-15 > 21 (+15) 5x > 36 (/5) x > 36/5 |
12-3x < 27 (-12)
-3x < 15 (/3) -x < 5 (/-1) x > -5 |
3x-5 < x+8 AND 5x > x-8
3x-5 < x+8 (-x) 5x > x-8 (-x)
2x-5 < 8 (+5) 4x > -8 (/4)
2x < 13 (/2) x > -2
x < 13/2
Therefore: -2 < x < 13/2
3x-5 < x+8 (-x) 5x > x-8 (-x)
2x-5 < 8 (+5) 4x > -8 (/4)
2x < 13 (/2) x > -2
x < 13/2
Therefore: -2 < x < 13/2
x-5 > 1-x AND 15-3x > 5+2x
x-5 > 1-x (+x) 15-3x > 5+2x (+3x)
2x-5 > 1 (+5) 15 > 5+5x (-5)
2x > 6 (/2) 10 > 5x (/5)
x > 3 2 > x
The two x values can never be equal, so you are left with two equations:-
x > 3 OR 2 > x
x-5 > 1-x (+x) 15-3x > 5+2x (+3x)
2x-5 > 1 (+5) 15 > 5+5x (-5)
2x > 6 (/2) 10 > 5x (/5)
x > 3 2 > x
The two x values can never be equal, so you are left with two equations:-
x > 3 OR 2 > x