GMAT Math : Algebra
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Example Questions
Example Question #461 : Algebra
Solve the following absolute value equation for 
No value for
No value for
In order to find the value of 
At this point, however, we cannot solve the equation any further. By definition, absolute value can never equal a negative number; therefore, there is no value for 
Example Question #21 : Absolute Value
Find the possible values of 
There are two ways to solve the absolute value portion of this problem:
From here, you can solve each of these equations independently to arrive at the correct answer:
The solution is 
Example Question #24 : Understanding Absolute Value
Solve for 
To solve an equation like |8x - 19| = 45, we set up two equations:
8x - 19 = 45 and 8x - 19 = -45.
Then it is simple arithmetic.
8x - 19 (+19) = 45 (+19)
8x/8 = 64/8
x = 8
8x - 19 (+19) = -45 (+19)
8x/8 = -26/8
x = -3.25
Therefore:
x = 8, -3.25
Example Question #25 : Understanding Absolute Value
Solve.
In order to solve for the values of 
When working with absolute value equations, however, we must remember that we are actually working with two equations:
Now we can solve for our values:
We can also write our answer as:
Remember, when dividing by a negative number, switch the direction of the inequality sign.
Example Question #465 : Algebra
If 
Four
Zero
Two
One
Three
Two
can be rewritten as
If 
Solve separately:
or
It is not necessary to solve these statements, as we can determine that the correct response is two solutions.
Example Question #31 : Absolute Value
Solve for 
To solve absolute value equations, we must set up two equations: one where the solution is negative, and one where the solution is positive.
Example Question #467 : Algebra
True or false: 
Statement 1:
Statement 2:
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
Assume Statement 1 alone.
Therefore, 
Assume Statement 2 alone. The sign of 
If 
Example Question #1551 : Gmat Quantitative Reasoning
How many values of
a true statement?
Four
None
One
Two
Three
Two
Therefore, if 
Either
The correct choice is therefore two.
Example Question #469 : Algebra
How many values of
a true statement?
Three
None
Four
Two
One
None
If the first equation is true, then
and
If the second equation is true, then
and
In each situation, the absolute value of an expression would be negative; since the absolute value of an expression cannot be negative, no solution is yielded.
There are no values of 
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