All GMAT Math Resources
Example Questions
Example Question #4 : Solving Inequalities
Solve .
must be positive, except when . When , .
Then we know that the inequality is only satisfied when , and . Therefore , which in interval notation is .
Note: Infinity must always have parentheses, not brackets. has a parentheses around it instead of a bracket because is less than , not less than or equal to .
Example Question #2 : Solving Inequalities
Solve .
The roots we need to look at are
:
Try
, so
does not satisfy the inequality.
:
Try
so does satisfy the inequality.
:
Try
so does not satisfy the inequality.
:
Try .
so satisfies the inequality.
Therefore the answer is and .
Example Question #3 : Solving Inequalities
Find the domain of .
all real numbers
all non-negative real numbers
all positive real numbers
We want to see what values of x satisfy the equation. is under a radical, so it must be positive.
Example Question #3 : Solving Inequalities
Solve the inequality:
When multiplying or dividing by a negative number on both sides of an inequality, the direction of the inequality changes.
Example Question #2 : Solving Inequalities
Find the solution set for :
Subtract 7:
Divide by -1. Don't forget to switch the direction of the inequality signs since we're dividing by a negative number:
Simplify:
or in interval form, .
Example Question #2 : Solving Inequalities
Which of the following is equivalent to ?
To solve this problem we need to isolate our variable .
We do this by subtracting from both sides and subtracting from both sides as follows:
Now by dividing by 3 we get our solution.
or
Example Question #4 : Solving Inequalities
How many integers satisfy the following inequality:
Five
Two
One
Three
Four
Two
There are two integers between 2.25 and 4.5, which are 3 and 4.
Example Question #118 : Algebra
What is the lowest value the integer can take?
The lowest value n can take is 6.
Example Question #11 : Solving Inequalities
What value of will make the following expression negative:
Our first step is to simplify the expression. We need to remember our order of operations or PEMDAS.
First distribute the 0.4 to the binomial.
Now distribute the 10 to the binomial.
Now multiply 0.6 by 5
Remember to flip the sign of the inequation when multiplying or dividing by a negative number.
220 will make the expression negative.
Example Question #120 : Algebra
Solve for .
To solve this problem all we need to do is solve for :