GRE Math : Equations / Inequalities

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Example Questions

Example Question #222 : Gre Quantitative Reasoning

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

Possible Answers:

All of the answers choices are valid.

-2

-1

-4

-3

Correct answer:

-1

Explanation:

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

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Example Question #223 : Gre Quantitative Reasoning

Solve for x

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

$\small 3x \geq -2x-3$

$\small 5x \geq -3$

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

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Example Question #181 : Equations / Inequalities

We have x^2-4<0 , find the solution set for this inequality.

Possible Answers:

x=0

x>-2

x<2

x>2, x<-2

-2<x<2

Correct answer:

-2<x<2

Explanation:

$x^2-4<0 \Rightarrow x^2<4 \Rightarrow -2<x<2$

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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:

None of the other answers are correct.

The rational expression is undefined.

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

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

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

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:

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

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

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Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality 2(x-1) > 3(2x+3) .

Possible Answers:

x < 4

$x < -\frac{11}{4}$

$x < -\frac{4}{11}$

$x > -\frac{11}{4}$

$x > -\frac{4}{11}$

Correct answer:

$x < -\frac{11}{4}$

Explanation:

Start by simplifying the expression by distributing through the parentheses to 2x-2 > 6x+9 .

Subtract from both sides to get -2 > 4x + 9 .

Next subtract 9 from both sides to get -11 > 4x . Then divide by 4 to get $-\frac{11}{4} > x$ which is the same as $x < -\frac{11}{4}$ .

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Example Question #3 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality 6(x-1) < 7(3-x) .

Possible Answers:

$x > -\frac{11}{17}$

$x > \frac{13}{27}$

$x < \frac{27}{13}$

$x > -\frac{13}{27}$

$x < \frac{12}{7}$

Correct answer:

$x < \frac{27}{13}$

Explanation:

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

This gives us 6x-6 < 21 -7x .

Add 6 to both sides to get 6x < 27-7x .

Add to both sides to get 13x < 27 .

Divide both sides by 13 to get $x < \frac{27}{13}$ .

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Example Question #226 : Gre Quantitative Reasoning

Quantitative Comparison

Quantity A: 3x + 4y

Quantity B: 4x + 3y

Possible Answers:

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

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!

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Example Question #21 : Inequalities

Let be an integer such that |x|<1 .

Quantity A: $x^{2}$

Quantity B:

Possible Answers:

Quantity A and Quantity B are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

Correct answer:

Quantity A and Quantity B are equal.

Explanation:

The expression |x|<1 can be rewritten as -1<x<1 .

The only integer that satisfies the inequality is 0.

Thus, Quantity A and Quantity B are equal.

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Example Question #3 : How To Find The Solution To An Inequality With Addition

Find all solutions of the inequality 2x + 3 < 5 .

Possible Answers:

All x < 2 .

All x > 1 .

All x < 1 ..

All x > 2 .

All x > 0 .

Correct answer:

All x < 1 ..

Explanation:

Start by subtracting 3 from each side of the inequality. That gives us 2x < 2 . Divide both sides by 2 to get x < 1 . Therefore every value for where x < 1 is a solution to the original inequality.

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Example Question #4 : How To Find The Solution To An Inequality With Addition

Find all solutions of the inequality 3x + 13 < x + 21 .

Possible Answers:

All x > 3 .

All x < 4 .

All x > 2 .

All x <2 .

All x > 4 .

Correct answer:

All x < 4 .

Explanation:

Start by subtracting 13 from each side. This gives us 3x < x + 8 . Then subtract from each side. This gives us 2x < 8 . Divide both sides by 2 to get x < 4 . Therefore all values of where x < 4 will satisfy the original inequality.

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GRE Math : Equations / Inequalities

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #222 : Gre Quantitative Reasoning

Example Question #223 : Gre Quantitative Reasoning

Example Question #181 : Equations / Inequalities

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

Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Example Question #3 : How To Find The Solution To An Inequality With Multiplication

Example Question #226 : Gre Quantitative Reasoning

Example Question #21 : Inequalities

Example Question #3 : How To Find The Solution To An Inequality With Addition

Example Question #4 : How To Find The Solution To An Inequality With Addition

All GRE Math Resources

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