Inequalities and Absolute values Flashcards
when do you need to reverse the inequality orientation?
when multiplying or dividing an inequality by a negative number
when inequalities can be added?
only if they have the same orientation
variable in an inequality rule
when you don’t know the sign of of an unknown variable, do not multiply or divide within an inequality
how do you compare the size of variables in an inequality equation?
by imagining their inequalities relations in a number line
how do you calculate minimum or maximum value of compound inequalities like a<=y<=b, c<=x<=d; ?
min value = min value (ac, ad, bc, bd)
max value = max value (ac, ad, bc, bd)
adding absolute values rule
|a+b| <= |a| + |b|
|a+b| = |a| + |b| when?
- when a or b is zero
- a and b have the same sign
subtracting absolute values rule
|a-b| >= |a| - |b|
|a-b| = |a| - |b| when?
- when b is zero
- |a| >= |b|
when do you check solutions in absolute value equations?
when you see variables on both LHS and RHS
How do you simplify x^2 > 4 and y^2 < 64?
x>2 or x<-2; -8<y<8
How do you simplify |x| > 4. and |y| < 2?
x>4 or x<-4; -2<y<2
when the absolute values are equal?
it must be true that expressions within the absolute bars are either equal or opposite
