GMAT Quant Chapter 5: Inequalities & Absolute Values Flashcards
When we divide or multiply an inequality by a negative sign, what happens?
The inequality sign flips
What must we do before adding two separate inequalities?
Both inequality signs must be facing the same direction
We never perform an operation to an inequality if we don’t know what?
The sign of the unknown.
Never multiply or divide an inequality unless the sign of the variable is known
What is a compound inequality?
A 3 part inequality where an unknown is defined in both directions
When manipulating a compound inequality, how do we maintain the original inequality?
Apply the operation to every individual part of the compound inequality.
What happens when we divide a compound inequality by a negative number?
We must reverse both of the inequality signs.
Which method of solving algebraic equations can we use to solve inequalities and in what order must we perform the operation?
Substitution.
isolate a variable in a separate equation and substitute the result into the inequality.
We cannot isolate a variable in an inequality and substitute that into an equation.
Which part of a compound inequality must we substitute an unknown variable equation into?
It does not matter as long as all manipulations afterwards are applied to all parts of the compound inequality
How should we solve when we are given lots of independent inequalities?
e.g. a > x x < y y < c
Draw a number line and visually see how they relate to each other.
How do we solve inequalities with squared variables?
Solve them like an equation but realise that the root of the squared number produces absolute values so we will often get two solutions.
What are the two solutions when x^2 > B and B > 0
X > Root B
or
X < - Root B
What are the two solutions when x^2 < B, and B > 0?
- Root B < x < Root B
How should we find the minimum and maximum values when we are given two compound inequalities?
evaluate the limits of the 4 inequalities given the smallest will be the minimum and the largest will be the maximum
How many times do we need to solve an equation that has absolute value bars?
Solve the equation twice. Once the absolute value bars are positive and once when they are negative.
How do we solve an equation that absolute value bars only around part of the expression?
Isolate the absolute value bars and put everything else together on the other side.
Then solve the absolute value bars twice.