GRE Math : How to find the solution to an inequality with addition
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Example Questions
Example Question #181 :Equations / Inequalities
Quantitative Comparison
Quantity A: 3x+ 4y
Quantity B: 4x+ 3y
Quantity B is greater.
The relationship cannot be determined from the information given.
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
The question does not give us any specifics about the variablesxandy.
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 #1 :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.
The relationship cannot be determined from the information given.
Quantity B is greater.
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 #22 :Inequalities
找到所有解决方案的不平等
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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
找到所有解决方案的不平等
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Start by subtracting 13 from each side. This gives us
Example Question #1 :How To Find The Solution To An Inequality With Addition
What values ofxmake the following statement true?
|x– 3| < 9
–3 <x< 9
6 <x< 12
x< 12
–6 <x< 12
–12 <x< 6
–6 <x< 12
Solve the inequality by adding 3 to both sides to getx< 12. Since it is absolute value,x- 3 > 9也必须解决了通过添加3 sides so:x> –6 so combined.
Example Question #11 :Inequalities
If –1 <w< 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
|w|0.5
w2
w/2
3w/2
|w|
3w/2
3w/2 will become greater than 1 as soon aswis greater than two thirds. It will likewise become less than –1 as soon aswis less than negative two thirds. All the other options always return values between –1 and 1.
Example Question #141 :Algebra
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 #21 :Inequalities
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 #5 :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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