GRE Math : How to find the solution to an inequality with multiplication

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Example Questions

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

Quantitative Comparison

x > 0

Column A:

Column B: $\frac{5}{x}$

Possible Answers:

The quantities are equal.

The relationship cannot be determined from the information provided.

Quantity B is greater.

Quantity A is greater.

Correct answer:

The relationship cannot be determined from the information provided.

Explanation:

For quantitative comparison questions involving a shared variable between quantities, the best approach is to test a positive integer, a negative integer, and a fraction. Half of our work is eliminated, however, because the question stipulates that x > 0. We only need to check a positive integer and a positive fraction between 0 and 1. Plugging in 2, we see that quantity A is greater than quantity B. Checking 1/2, however, we find that quantity B is greater than quantity A. Thus the relationship cannot be determined.

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

If –1 < n < 1, all of the following could be true EXCEPT:

Possible Answers:

(n-1)² > n

|n² - 1| > 1

16n² - 1 = 0

n² < n

n² < 2n

Correct answer:

|n² - 1| > 1

Explanation:

N_part_1

N_part_2

N_part_3

N_part_4

N_part_5

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

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

Possible Answers:

-4

-1

-3

-2

All of the answers choices are valid.

Correct answer:

-1

Explanation:

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

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

Solve for x

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

Possible Answers:

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

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

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

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

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 #33 : Inequalities

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

Possible Answers:

x>2, x<-2

x<2

x>-2

-2<x<2

x=0

Correct answer:

-2<x<2

Explanation:

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

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Example Question #3 : 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 #21 : Inequalities

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

Possible Answers:

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

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

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

x < 4

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

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:

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

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

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

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

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

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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GRE Math : How to find the solution to an inequality with multiplication

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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 #2 : 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 #33 : Inequalities

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

Example Question #21 : Inequalities

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

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