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GRE Subject Test: Math : Inequalities

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

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Example Questions

Example Question #224 : Gre Subject Test: Math

0.6x +1.2 > 4.8

Possible Answers:

x>10

x<6

x>6

x<10

Correct answer:

x>6

Explanation:

0.6x + 1.2 > 4.8

10 (0.6x +1.2) > 4.8 (10)

6x + 12 > 48

6x + 12 - 12 = 48 -12

6x > 36

$\frac{6x}{6}> \frac{36}{6}$

x> 6

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Example Question #22 : Solving Inequalities

$12\left ( \frac{x+3}{2} -\frac{3x-2}{4}\right ) < 12x-1$

Possible Answers:

x < 2

$x< \frac{1}{2}$

x< -2

$x> \frac{5}{3}$

Correct answer:

$x> \frac{5}{3}$

Explanation:

$12\left ( \frac{x+3}{2} -\frac{3x-2}{4}\right ) < 12x-1$

$12\left ( \frac{2x+6}{4} -\frac{3x-2}{4}\right ) < 12x-1$

$12\left ( \frac{-x+8}{4}\right ) < 12x-1$

3(-x+8) < 12x-1

-3x +24 < 12x-1

25 < 15x

$x>\frac{25}{15} \rightarrow x>\frac{5}{3}$

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Example Question #23 : Solving Inequalities

Solve for the values of x that satisfies the equation: $2x-3\leqslant 9$ .

Possible Answers:

$x\leq6$

x<6

x<-6

$x\geq6$

Correct answer:

$x\leq6$

Explanation:

Step 1: Move the constant from the left side to the right side. We have , so we will add 3 to both sides of the equation to move the constant over.

$2x-3+(3)\leqslant9+3\rightarrow 2x\leqslant12$

Step 2: Divide by the coefficient in front of x.

$\frac {2x}{2}\leqslant \frac {12}{2}\rightarrow x\leqslant 6$

The values of x that satisfy the equation are $x\leqslant6$ (or $x\leq6$ )

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Example Question #43 : Algebra

7+4x>-3x+4

Possible Answers:

x=3/7

x>3/7

x<-3/7

x>-3/7

x<3/7

Correct answer:

x>-3/7

Explanation:

This problem involves solving the inequality.

7+4x>-3x+4

Add 3x to both sides

7+7x>+4

Subtract 7 to each side

7x>-3

divide both sides by7

x>-3/7

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Example Question #44 : Algebra

31>7x+3>2x+6

4>x>3/5

Possible Answers:

x<4

4>x>5/3

3/2>x>1/2

x>3/5

Unsolvable

Correct answer:

3/2>x>1/2

Explanation:

To solve this inequality you must first break apart the inequality into two seperate inequalities.

31>7x+3

subtract the three from both sides

28>7x

divide seven on both sides

4>x

7x+3>2x+6

subtract 2x from both sides

5x+3>6

Subtract 3 from both sides

5x>3

Divide by 5 on both sides

5x>3

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Example Question #21 : Inequalities

$Solve\ for\ x: 3x-12>-9$

Possible Answers:

x>-7

x<-7

x>1

x<1

Correct answer:

x>1

Explanation:

$3x-12>-9\ Add\ 12\ to\ both\ sides\\ \\$

$3x>3\ divide\ both\ sides\ by\ 3$

x>1

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Example Question #24 : Solving Inequalities

$Solve\ for\ x:\\$

5-2x>13

Possible Answers:

x>-4

x<-4

x>-9

x<-9

Correct answer:

x<-4

Explanation:

$5-2x>13\ subtract\ 5\ from\ both\ sides$

$-2x>8\ divide\ both\ sides\ by\ (-2)$

$x<-4\ when\ dividing\ by\ a\ negative\ make\ sure\ you\ flip\ the\ inequality\ sign$

$We\ flip\ the\ inequality\ sign\ because\ the\ sign\ on\ both\ sides\ changed.$

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Example Question #27 : Solving Inequalities

4x + 12 < x + 21

Possible Answers:

all values of where $x\geq 3$

all values of where x< 3

all values of where x> 3

all values of where $x\leq 3$

Correct answer:

all values of where x< 3

Explanation:

4x + 12 < x + 21

Subtract 12 from both sides of the inequality.

4x + 12 - 12< x + 21 - 12

4x < x + 9

Subtract from both sides of the inequality.

4x - x< x-x -9

3x < 9

Divide both sides by 3.

$\frac{3x}{3} < \frac{9}{3}$

x < 3

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Example Question #22 : Inequalities

$5\left | x-7\right |+14<39$

Possible Answers:

2< x<12

x> 12 or x< 2

x<12

2< x

Correct answer:

2< x<12

Explanation:

The first thing we must do is get the absolute value alone: $5\left | x-7\right |+14<39$

$5\left | x-7\right |<25$

$\left | x-7\right |<5$

When we're working with absolute values, we are actually solving two equations:

x-7<5 and x-7> -5

Fortunately, these can be written as one equation:

-5< x-7<5

If you feel more comfortable solving the equations separately then go ahead and do so.

2< x<12

To get alone, we added on both sides of the inequality sign

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Example Question #23 : Inequalities

$\left | y\right | + 18 \leq 11.3$

Possible Answers:

$y\leq 29.3$

$y\leq -6.7$

$y\geq 6.7$

There is no solution.

Correct answer:

There is no solution.

Explanation:

$\left | y\right | + 18 \leq 11.3$

$\left | y\right |\leq -6.7$

Because Absolute Value must be a non-negative number, there is no solution to this Absolute Value inequality.

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GRE Subject Test: Math : Inequalities

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #224 : Gre Subject Test: Math

Example Question #22 : Solving Inequalities

Example Question #23 : Solving Inequalities

Example Question #43 : Algebra

Example Question #44 : Algebra

Example Question #21 : Inequalities

Example Question #24 : Solving Inequalities

Example Question #27 : Solving Inequalities

Example Question #22 : Inequalities

Example Question #23 : Inequalities

All GRE Subject Test: Math Resources

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