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GRE Subject Test: Math : Algebra

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

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All GRE Subject Test: Math Resources

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Example Questions

Example Question #31 : Algebra

$3\leq 9 +c$

Possible Answers:

$c\geq 6$

$c\leq -6$

$c\leq 6$

$c\geq -6$

Correct answer:

$c\geq -6$

Explanation:

$3\leq 9 +c$

Subtract 9 from both sides of the inequality.

$3-9 \leq (9-9) + c$

$-6 \leq c$

Because the variable, in this case is to the right of the inequality sign, you switch the inequality sign to its opposite. The $\leq$ becomes a $\geq$ so that the variable is to the left of the inequality sign.

$c\geq -6$

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Example Question #31 : Classifying Algebraic Functions

$y + \frac{2}{3} > 7$

Possible Answers:

$y\geq 6 \frac{1}{3}$

$y> 6\frac{1}{3}$

$y \geq 7\frac{2}{3}$

$y< 6\frac{1}{3}$

Correct answer:

$y> 6\frac{1}{3}$

Explanation:

$y + \frac{2}{3} > 7$

Subtract $\frac{2}{3}$ from both sides of the inequality.

$y + \frac{2}{3} - \frac{2}{3} > 7 - \frac{2}{3}$

$y> 6\frac{1}{3}$

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Example Question #11 : Inequalities

-12 > z-4

Possible Answers:

z< -8

z> -8

$z\leq -8$

$z\geq -8$

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 #32 : Classifying Algebraic Functions

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

Possible Answers:

$n\leq 13$

$n\leq 7$

$n\geq 13$

$n\leq 6$

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 #33 : Classifying Algebraic Functions

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

Possible Answers:

-8<x< 8

x = 0

x < 8

8< x<8

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 #34 : Classifying Algebraic Functions

b - 6 > 13

Possible Answers:

b > 19

b> 7

b< 19

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

Report an Error

Example Question #35 : Classifying Algebraic Functions

Solve.

$12 + n \leq 4$

Possible Answers:

$n \leq -12$

$n\leq 12$

$n\leq 8$

$n\leq -8$

Correct answer:

$n\leq -8$

Explanation:

$12+n\leq 4$

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

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

$n\leq -8$

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GRE Subject Test: Math : Algebra

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #31 : Algebra

Example Question #31 : Classifying Algebraic Functions

Example Question #11 : Inequalities

Example Question #34 : Algebra

Example Question #32 : Classifying Algebraic Functions

Example Question #33 : Classifying Algebraic Functions

Example Question #37 : Algebra

Example Question #34 : Classifying Algebraic Functions

Example Question #14 : Solving Inequalities

Example Question #35 : Classifying Algebraic Functions

All GRE Subject Test: Math Resources

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