Quant Ch 5 - Inequities & Absolute Value Flashcards
Open circle on number line
greater/less than
Closed circle on number line
greater/less than equal to
Multiplying/dividing an inequity by a negative number
Flip the inequity sign when you multiply or divide by a negative number
Adding inequities
When the sign faces the same direction, multiple inequities can be added
Compound inequity
combining 2 inequities. If the compound inequity is multiplied or divided by a (-) number, both signs must be flipped
Ex/ x < 5 , x > -4 –> -4 < x < 5
If x² > B and B is positive
x > √b or x < -√b
If x² ≥ B and B is positive
x ≥ √b or x ≤ -√b
If x² > B and B is positive
-√b < x < √b
If x² ≥ B and B is positive
-√b ≤ x ≤ √b
Finding the min and max value of xy
If a ≤ x ≤ b, solve ac, ad, bc, and bd. The largest value is the max and the smallest is the min
Absolute value
For any real number a:
|a| = |-a|
if a ≥ 0, then |a|= a
if a < 0, then |a| = -a
Rule for equations with absolute value signs
When solving equations with absolute values, make sure to solve for both the positive and negative value of the answer
When 2 absolute values are equal to each other
If |x| = |y|, then x = y or -x = -y
Adding absolute values
|a+b| ≤ |a| + |b|
If a and b are non-zero numbers and |a+b|=|a|+|b|, then a. and b must have the same sign
Subtracting absolute values
|a-b|≥|a|-|b|
If b≠0 and|a-b|=|a|-|b|, then a and b must have the same sign and |a|≥|b|
