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GRE Subject Test: Math : Solving Inequalities

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #11 : Inequalities

-12 > z-4

Possible Answers:

$z\leq -8$

z> -8

$z\geq -8$

z< -8

Correct answer:

z< -8

Explanation:

-12 > z-4

Add 4 to both sides of the inequality.

-12 + 4> z-4 + 4

-8 > z

Because the variable is to the right of the inequality, it needs to be placed to the left of the inequality. When this happens, the inequality sign needs to be switched to its opposite.

z < -8

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Example Question #34 : Algebra

$3x +6\geq -2x + 8$

Possible Answers:

$x\geq \frac{2}{5}$

$x\leq \frac{5}{2}$

$x\geq \frac{5}{2}$

$x\leq \frac{2}{5}$

Correct answer:

$x\geq \frac{2}{5}$

Explanation:

$3x + 6 \geq -2x + 8$

Subtract 6 from both sides of the inequality.

$3x + 6 - 6\geq -2x + 8 - 6$

$3x\geq -2x + 2$

Add to both sides of the inequality.

$3x + 2x\geq -2x + 2x + 2$

$5x \geq 2$

Divide both sides by .

$\frac{5x}{5} \geq \frac{2}{5}$

$x\geq \frac{2}{5}$

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Example Question #11 : Inequalities

The difference between a number and 6 is no more than 7. What would those numbers be?

Possible Answers:

$n\geq 13$

$n\leq 6$

$n\leq 7$

$n\leq 13$

Correct answer:

$n\leq 13$

Explanation:

$n - 6\leq 7$

Would be the inequality that represents that statement.

Add to both sides of that inequality.

$n - 6 + 6 \leq 13$

$n\leq 13$

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Example Question #12 : Inequalities

$x^{2} -64< 0$ Find the solution set.

Possible Answers:

8< x<8

x < 8

-8<x< 8

x = 0

Correct answer:

-8<x< 8

Explanation:

$x^{2} - 64< 0$

$x^{2} < 64$

-8 < x < 8

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Example Question #37 : Algebra

3 (x-3) > 4 (x+2)

Possible Answers:

x< 17

x> -1

x< -1

x < -17

Correct answer:

x < -17

Explanation:

3 (x-3) > 4(x+2)

Begin by simplifying the inequality by using the distributive property.

3x - 9 > 4x +8

Add to both sides.

3x-9 + 9 > 4x + 8 + 9

3x> 4x + 17

Subtract from both sides.

3x-4x > 4x-4x+17

-x > 17

Because there is a negative variable, multiply both sides by and switch the inequality sign to its opposite.

x< -17

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Example Question #13 : Inequalities

b - 6 > 13

Possible Answers:

b > 19

b< 19

b<7

b> 7

Correct answer:

b > 19

Explanation:

b - 6 > 13

Add 6 to both sides of the inequality.

b-6 + 6> 13 + 6

b> 19

Report an Error

Example Question #14 : Solving Inequalities

-3x -12> 15

Possible Answers:

x> -9

x < -9

x< 9

$x\geq 9$

Correct answer:

x < -9

Explanation:

-3x-12> 15

To isolate the variable, add to both sides of the inequality.

-3x-12+12 > 15 + 12

-3x >27

Divide both sides by -3. Because you are dividing by a negative integer, you have to flip or switch the inequality sign to its opposite.

x < -9

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Example Question #14 : Inequalities

Solve.

$12 + n \leq 4$

Possible Answers:

$n\leq -8$

$n\leq 12$

$n \leq -12$

$n\leq 8$

Correct answer:

$n\leq -8$

Explanation:

$12+n\leq 4$

To isolate the variable , subtract from both sides of the inequality.

$(12-12) + n \leq4-12$

$n\leq -8$

Report an Error

Example Question #15 : Inequalities

$x + 0.8\leq -0.5$

Possible Answers:

$x\leq 1.3$

$x\leq 0.3$

$x\leq -0.3$

$x\leq -1.3$

Correct answer:

$x\leq -1.3$

Explanation:

$x + 0.8\leq -0.5$

To isolate the variable, subtract 0.8 from both sides of the inequality.

$x + 0.8-0.8 \leq -0.5-0.8$

$x\leq -1.3$

Report an Error

Example Question #42 : Algebra

8x-10 > 4x - 6

Possible Answers:

x<3

x>3

x>1

x> -1

Correct answer:

x>1

Explanation:

8x-10 > 4x-6

Subtract from both sides of the equation

8x-4x-10 > 4x-4x-6

4x -10> -6

Add to both sides of the equation.

4x-10 + 10 = -6 + 10

4x > 4

Divide both sides by 4.

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

x>1

Report an Error

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GRE Subject Test: Math : Solving Inequalities

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Inequalities

Example Question #34 : Algebra

Example Question #11 : Inequalities

Example Question #12 : Inequalities

Example Question #37 : Algebra

Example Question #13 : Inequalities

Example Question #14 : Solving Inequalities

Example Question #14 : Inequalities

Example Question #15 : Inequalities

Example Question #42 : Algebra

All GRE Subject Test: Math Resources

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