All GMAT Math Resources
Example Questions
Example Question #431 : Algebra
Solve for .
In order to solve this problem, we need to combine like terms and then factor:
Example Question #432 : Algebra
Solve for :
To solve this we must factor:
The first step is to recognize that all of the terms on the equation's left side contain 4x. Therefore we can pull 4x out:
Then we factor the inside of the parentheses, realizing that only -3, and -4 add to form -7, and multiply to form 12:
Now we can see that, for the left side of the equation to equal zero, x can only equal 0, 3, or 4.
Example Question #431 : Algebra
Solve the following by factoring:
To solve, divide out a and then factor.
Example Question #432 : Algebra
Simplify .
Example Question #1 : Absolute Value
Solve .
or
or
or
or
really consists of two equations:
We must solve them both to find two possible solutions.
So or .
Example Question #2 : Absolute Value
Solve .
It's actually easier to solve for the complement first. Let's solve . That gives -3 < 2x - 5 < 3. Add 5 to get 2 < 2x < 8, and divide by 2 to get 1 < x < 4. To find the real solution then, we take the opposites of the two inequality signs. Then our answer becomes .
Example Question #3 : Absolute Value
Give the -intercept(s), if any, of the graph of the function in terms of .
Set and solve for :
Rewrite as a compound equation and solve each part separately:
Example Question #4 : Absolute Value
A number is ten less than its own absolute value. What is this number?
No such number exists.
We can rewrite this as an equation, where is the number in question:
A nonnegative number is equal to its own absolute value, so if this number exists, it must be negative.
In thsi case, , and we can rewrite that equation as
This is the only number that fits the criterion.
Example Question #1 : Understanding Absolute Value
If , which of the following has the greatest absolute value?
Since , we know the following:
;
;
;
;
.
Also, we need to compare absolute values, so the greatest one must be either or .
We also know that when .
Thus, we know for sure that .
Example Question #6 : Absolute Value
Give all numbers that are twenty less than twice their own absolute value.
No such number exists.
We can rewrite this as an equation, where is the number in question:
If is nonnegative, then , and we can rewrite this as
Solve:
If is negative, then , and we can rewrite this as
The numbers have the given characteristics.