How to find the solution to an inequality with subtraction - GRE Quantitative Reasoning
Card 0 of 5
and 
are both integers.
If 
, 
, and 
, which of the following is a possible value of 
?
If
Take the values of y that are possible, i.e. 2 and 3, and plug them into the first inequality. First, plug in 2. 2 – 3x > 21. Subtract 2 from both sides, and then divide by –3. Don't forget that when you divide or multiply by a negative number in an inequality you must flip the inequality sign. Thus, x < –19/3. Now plug in 3. We find, following the same steps, that when y=3, x < –6. Thus –7 is the correct answer.
Take the values of y that are possible, i.e. 2 and 3, and plug them into the first inequality. First, plug in 2. 2 – 3x > 21. Subtract 2 from both sides, and then divide by –3. Don't forget that when you divide or multiply by a negative number in an inequality you must flip the inequality sign. Thus, x < –19/3. Now plug in 3. We find, following the same steps, that when y=3, x < –6. Thus –7 is the correct answer.
Compare your answer with the correct one above
The cost, in cents, of manufacturing 
pencils is 
, where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?
The cost, in cents, of manufacturing
If each pencil sells at 50 cents, 
pencils will sell at 
. The smallest value of 
such that
If each pencil sells at 50 cents,
Compare your answer with the correct one above
Find the slope of the inequality equation 
Find the slope of the inequality equation
The answer is:
From the equation we can see that the slope is –1.
The answer is:
From the equation we can see that the slope is –1.
Compare your answer with the correct one above
Quantity A:
The value(s) for which the following function is undefined:
Quantity B:
Which of the following is true?
Quantity A:
The value(s) for which the following function is undefined:
Quantity B:
Which of the following is true?
This question is not as hard as it seems. Remember that for real numbers, square roots cannot be taken of negative numbers. Therefore, we know that this function is undefined for:
This is simple to solve. Merely add 
to both sides:
Then, divide by 
:
Therefore, quantity A is less than quantity B. This means that quantity B is greater than it.
This question is not as hard as it seems. Remember that for real numbers, square roots cannot be taken of negative numbers. Therefore, we know that this function is undefined for:
This is simple to solve. Merely add
Then, divide by
Therefore, quantity A is less than quantity B. This means that quantity B is greater than it.
Compare your answer with the correct one above
Quantity A:
Quantity B:
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
Recall that when you have an absolute value and an inequality like
,
this is the same as saying that 
must be between 
and 
. You can rewrite it:
To solve this, you merely need to subtract 
from all three values:
Since 
is between 
and 
, it could be both larger or smaller than 
. Therefore, you cannot determine the relationship based on the given information.
Recall that when you have an absolute value and an inequality like
this is the same as saying that
To solve this, you merely need to subtract
Since
Compare your answer with the correct one above