GRE Math : How to find the solution to an inequality with addition
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Example Questions
Example Question #1 : How To Find The Solution To An Inequality With Addition
Quantitative Comparison
Quantity A: 3x + 4y
Quantity B: 4x + 3y
The two quantities are equal.
The relationship cannot be determined from the information given.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The question does not give us any specifics about the variables x and y.
If we substitute the same numbers for x and y (say, x = 1 and y = 1), the two expressions are equal.
If we substitute different number in for x and y (say, x = 2 and y = 1), the two expressions are not equal.
If there are two possible outcomes, then we need more information to determine which quantity is greater. Don't be afraid to pick "The relationship cannot be determined from the information given" as an answer choice on the GRE!
Example Question #2 : How To Find The Solution To An Inequality With Addition
Let 
Quantity A: 
Quantity B:
Quantity A and Quantity B are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
Quantity A and Quantity B are equal.
The expression 
The only integer that satisfies the inequality is 0.
Thus, Quantity A and Quantity B are equal.
Example Question #3 : How To Find The Solution To An Inequality With Addition
Find all solutions of the inequality 
All 
All 
All 
All 
All 
All
Start by subtracting 3 from each side of the inequality. That gives us 
Example Question #4 : How To Find The Solution To An Inequality With Addition
Find all solutions of the inequality 
All 
All 
All 
All 
All 
All
Start by subtracting 13 from each side. This gives us 
Example Question #3 : How To Find The Solution To An Inequality With Addition
What values of x make the following statement true?
|x – 3| < 9
6 < x < 12
–12 < x < 6
x < 12
–6 < x < 12
–3 < x < 9
–6 < x < 12
Solve the inequality by adding 3 to both sides to get x < 12. Since it is absolute value, x – 3 > –9 must also be solved by adding 3 to both sides so: x > –6 so combined.
Example Question #4 : How To Find The Solution To An Inequality With Addition
If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
w2
|w|
|w|0.5
w/2
3w/2
3w/2
3w/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.
Example Question #5 : How To Find The Solution To An Inequality With Addition
Solve for 
Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.
Example Question #2 : How To Find The Solution To An Inequality With Addition
If 
To solve this problem, add the two equations together:
The only answer choice that satisfies this equation is 0, because 0 is less than 4.
Example Question #1 : How To Find The Solution To An Inequality With Addition
What values of 
First, solve the inequality 
Since we are dealing with absolute value, 
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