GRE Math : Equations / Inequalities

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #11 : Inequalities

(√(8) / -x ) <  2. Which of the following values could be x?

Possible Answers:

-4

-3

All of the answers choices are valid.

-2

-1

Correct answer:

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

Example Question #51 : New Sat Math Calculator

Solve for x

\small 3x+7 \geq -2x+4

 

Possible Answers:

\small x \geq -\frac{3}{5}

\small x \geq \frac{3}{5}

\small x \leq \frac{3}{5}

\small x \leq -\frac{3}{5}

Correct answer:

\small x \geq -\frac{3}{5}

Explanation:

\small 3x+7 \geq -2x+4

\small 3x \geq -2x-3

\small 5x \geq -3

\small x\geq -\frac{3}{5}

Example Question #5 : How To Find The Solution To An Inequality With Multiplication

We have , find the solution set for this inequality. 

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Fill in the circle with either <, >, or = symbols:

(x-3)\circ\frac{x^2-9}{x+3} for x\geq 3.

 

Possible Answers:

(x-3)< \frac{x^2-9}{x+3}

The rational expression is undefined.

(x-3)> \frac{x^2-9}{x+3}

(x-3)=\frac{x^2-9}{x+3}

None of the other answers are correct.

Correct answer:

(x-3)=\frac{x^2-9}{x+3}

Explanation:

(x-3)\circ\frac{x^2-9}{x+3}

Let us simplify the second expression. We know that:

(x^2-9)=(x+3)(x-3)

So we can cancel out as follows:

\frac{x^2-9}{x+3}=\frac{(x+3)(x-3)}{(x+3)}=x-3

(x-3)=\frac{x^2-9}{x+3}

 

Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality .

Possible Answers:

Correct answer:

Explanation:

Start by simplifying the expression by distributing through the parentheses to .

Subtract  from both sides to get .

Next subtract 9 from both sides to get . Then divide by 4 to get  which is the same as .

Example Question #1 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality .

Possible Answers:

Correct answer:

Explanation:

Start by simplifying each side of the inequality by distributing through the parentheses.

This gives us .

Add 6 to both sides to get .

Add  to both sides to get .

Divide both sides by 13 to get .

Example Question #1 : How To Find The Solution To An Inequality With Addition

Quantitative Comparison

Quantity A: 3x + 4y

Quantity B: 4x + 3y

Possible Answers:

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

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 #1 : How To Find The Solution To An Inequality With Addition

Let  be an integer such that .

Quantity A:           

Quantity B: 


                        

Possible Answers:

The relationship cannot be determined from the information given.

Quantity A and Quantity B are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A and Quantity B are equal.

Explanation:

The expression  can be rewritten as .

The only integer that satisfies the inequality is 0.

Thus, Quantity A and Quantity B are equal. 

Example Question #181 : Equations / Inequalities

Find all solutions of the inequality .

Possible Answers:

All .

All ..

All .

All .

All .

Correct answer:

All ..

Explanation:

Start by subtracting 3 from each side of the inequality. That gives us . Divide both sides by 2 to get . Therefore every value for  where  is a solution to the original inequality.

Example Question #21 : Inequalities

Find all solutions of the inequality .

Possible Answers:

All .

All .

All .

All .

All .

Correct answer:

All .

Explanation:

Start by subtracting 13 from each side. This gives us . Then subtract  from each side. This gives us . Divide both sides by 2 to get . Therefore all values of  where  will satisfy the original inequality.

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