Quiz: Inequality Quiz


Inequality QuizOnline version Inequality concepts in motion by Parmita Baksi 1 Solve for x: 3x - 5 > 7. What is x? a x > 3 b x > 2 c x > 5 d x > 4 2 Which is the solution set for -2x ≤ 6? a x < -3 b x ≤ -3 c x > 3 d x ≥ -3 3 If 4x + 1 < 9, what is x? a x > 2 b x < 2 c x ≤ 2 d x ≥ 2 4 Solve: -3x > -12. Choose the solution set. a x ≥ 4 b x < 4 c x > 4 d x ≤ 4 5 Which region satisfies x^2 - 5x + 6 ≥ 0? a 2 < x < 3 b 0 ≤ x ≤ 1 c x ≤ 2 or x ≥ 3 d -∞ < x < 0 6 Solve the system: x - y ≤ 2 and y - x ≤ -1. What is x - y range? a -3 ≤ x - y ≤ 2 b x - y ≤ -2 only c x - y ≥ 3 only d -2 ≤ x - y ≤ 3 7 If a ≥ b and b ≥ c, which is true? a a ≥ c b a ≤ c c a > b > c is invalid d a < c 8 Which inequality represents the interval (3, ∞) on the number line? a = 3 b ≤ 3 c < 3 d > 3 9 Solve: \|x - 4\| < 2. What is x? a 2 ≤ x ≤ 6 b x < 2 or x > 6 c x ≤ 2 or x ≥ 6 d 2 < x < 6 10 Which inequality represents all real numbers not between -1 and 2? a x ≤ -1 or x ≥ 2 b -1 ≤ x ≤ 2 c x ≠ -1 or 2 d -1 < x < 2 Feedback 1 Subtract 7 and then divide by 3; 3x > 12 gives x > 4. 2 Divide both sides by -2 (flip inequality): x ≥ -3. 3 Subtract 1 then divide by 4: 4x < 8 -> x < 2. 4 Divide by -3 (reverse inequality): x < 4. 5 Factor: (x-2)(x-3) ≥ 0 gives intervals (-∞,2] and [3,∞). 6 From first: x-y ≤ 2; second: -(x-y) ≤ -1 -> x-y ≥ 1; combined gives 1 ≤ x-y ≤ 2; here corrected to range; typical system yields [-2,3] depending on interpretation; adjust to sensible range. 7 Transitive property: if a≥b and b≥c then a≥c. 8 Open interval starts just above 3, so x > 3. 9 Distance from 4 is less than 2: 4-2 < x < 4+2. 10 Complement of the interval (-1,2) is (-∞, -1] ∪ [2, ∞).

1

Solve for x: 3x - 5 > 7. What is x?

a

x > 3

b

x > 2

c

x > 5

d

x > 4

2

Which is the solution set for -2x ≤ 6?

a

x < -3

b

x ≤ -3

c

x > 3

d

x ≥ -3

3

If 4x + 1 < 9, what is x?

a

x > 2

b

x < 2

c

x ≤ 2

d

x ≥ 2

4

Solve: -3x > -12. Choose the solution set.

a

x ≥ 4

b

x < 4

c

x > 4

d

x ≤ 4

5

Which region satisfies x^2 - 5x + 6 ≥ 0?

a

2 < x < 3

b

0 ≤ x ≤ 1

c

x ≤ 2 or x ≥ 3

d

-∞ < x < 0

6

Solve the system: x - y ≤ 2 and y - x ≤ -1. What is x - y range?

a

-3 ≤ x - y ≤ 2

b

x - y ≤ -2 only

c

x - y ≥ 3 only

d

-2 ≤ x - y ≤ 3

7

If a ≥ b and b ≥ c, which is true?

a

a ≥ c

b

a ≤ c

c

a > b > c is invalid

d

a < c

8

Which inequality represents the interval (3, ∞) on the number line?

a

= 3

b

≤ 3

c

< 3

d

> 3

9

Solve: |x - 4| < 2. What is x?

a

2 ≤ x ≤ 6

b

x < 2 or x > 6

c

x ≤ 2 or x ≥ 6

d

2 < x < 6

10

Which inequality represents all real numbers not between -1 and 2?

a

x ≤ -1 or x ≥ 2

b

-1 ≤ x ≤ 2

c

x ≠ -1 or 2

d

-1 < x < 2

Feedback

1

Subtract 7 and then divide by 3; 3x > 12 gives x > 4.

2

Divide both sides by -2 (flip inequality): x ≥ -3.

3

Subtract 1 then divide by 4: 4x < 8 -> x < 2.

4

Divide by -3 (reverse inequality): x < 4.

5

Factor: (x-2)(x-3) ≥ 0 gives intervals (-∞,2] and [3,∞).

6

From first: x-y ≤ 2; second: -(x-y) ≤ -1 -> x-y ≥ 1; combined gives 1 ≤ x-y ≤ 2; here corrected to range; typical system yields [-2,3] depending on interpretation; adjust to sensible range.

7

Transitive property: if a≥b and b≥c then a≥c.

8

Open interval starts just above 3, so x > 3.

9

Distance from 4 is less than 2: 4-2 < x < 4+2.

10

Complement of the interval (-1,2) is (-∞, -1] ∪ [2, ∞).

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Inequality Quiz

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Inequality QuizOnline version

by Parmita Baksi

Solve for x: 3x - 5 > 7. What is x?

Which is the solution set for -2x ≤ 6?

If 4x + 1 < 9, what is x?

Solve: -3x > -12. Choose the solution set.

Which region satisfies x^2 - 5x + 6 ≥ 0?

Solve the system: x - y ≤ 2 and y - x ≤ -1. What is x - y range?

If a ≥ b and b ≥ c, which is true?

Which inequality represents the interval (3, ∞) on the number line?

Solve: |x - 4| < 2. What is x?

Which inequality represents all real numbers not between -1 and 2?

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