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# How many integers are in the solution set of the inequality

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Joined: 07 Jun 2014
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How many integers are in the solution set of the inequality [#permalink]  20 May 2016, 18:02
Expert's post
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Question Stats:

45% (00:36) correct 55% (00:50) wrong based on 40 sessions
How many integers are in the solution set of the inequality $$x^2 - 10 < 0$$?

A. Two
B. Five
C. Six
D. Seven
E. Ten

Practice Questions
Question: 11
Page: 83
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 128

Kudos [?]: 2045 [0], given: 397

Re: How many integers are in the solution set of the inequality [#permalink]  20 May 2016, 18:05
Expert's post
Explanation

The inequality $$x^2 - 10 < 0$$ is equivalent to $$x^2 < 10$$. By inspection, the positive integers that satisfy this inequality are 1, 2, and 3. Note that 0 and the negative integers –1, –2, and –3 also satisfy the inequality, and there are no other integer solutions. So there are seven integers in the solution set: –3, –2, –1, 0, 1, 2, and 3.

Thus the correct answer is Choice D.
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Sandy
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Re: How many integers are in the solution set of the inequality [#permalink]  23 May 2016, 16:23
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Expert's post
sandy wrote:
How many integers are in the solution set of the inequality $$x^2 - 10 < 0$$?

A. Two
B. Five
C. Six
D. Seven
E. Ten

We can simplify the inequality to:

x^2 < 10

√x^2 < √10

|x| < √10

We can rewrite the square root of 10 as 3.2 (the estimated value of √10)

|x| < 3.2

Finally, we can solve for when x is positive and negative.

When x is positive:

x < 3.2

When x is negative:

-x < 3.2

x > -3.2

Thus, -3.2 < x < 3.2

The integers that satisfy the inequality are -3, -2, -1, 0, 1, 2, and 3. So 7 integers satisfy the inequality.

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Re: How many integers are in the solution set of the inequality [#permalink]  23 May 2016, 19:51
1
KUDOS
The x is between - square root of 10 and + square root of 10. As x is an integer, all integers from -3 to +3 are values of x, hence the answer is 7
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Re: How many integers are in the solution set of the inequality [#permalink]  12 Jun 2019, 09:15
Expert's post
sandy wrote:
How many integers are in the solution set of the inequality $$x^2 - 10 < 0$$?

A. Two
B. Five
C. Six
D. Seven
E. Ten

Practice Questions
Question: 11
Page: 83

Take: $$x^2 - 10 < 0$$
Add 10 to both sides: $$x^2 < 10$$

Let's test some POSITIVE values.
x = 2 satisfies the equation, since $$2^2 < 10$$
x = 3 satisfies the equation, since $$3^2 < 10$$
However, x = 4 does NOT satisfy the equation, since $$4^2 > 10$$
So, the biggest integer value of x is 3.

Let's test some NEGATIVE values.
x = -2 satisfies the equation, since $$(-2)^2 < 10$$
x = -3 satisfies the equation, since $$(-3)^2 < 10$$
However, x = -4 does NOT satisfy the equation, since $$(-4)^2 > 10$$
So, the smallest integer value of x is -3.

When we combine the results, we can see that can be any integer value from -3 to 3 inclusive.
In other words, x can be -3, -2, -1, 0, 1, 2 or 3 (seven possible values)

Cheers,
Brent
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Re: How many integers are in the solution set of the inequality   [#permalink] 12 Jun 2019, 09:15
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# How many integers are in the solution set of the inequality

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