Inequalities Test

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Inequalities Test - 1

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Weekly Quiz Competition

Question 1
3 / -1

For which values of x does this equation stands true: 3x² – 7x – 6 < 0

A
–2 < x < 2

B
x < – 0.66 or x > 3

C
3 < x < 7

D
–0.66 < x < 3
Solution
At x = 0, inequality is satisfied. Hence, options (b) and (c) are rejected.
x = 3 gives LHS = RHS and x = -0.66 also does the same.
Hence roots of the equation are 3 and -0.66. Thus, option (d) is correct.
Question 2
3 / -1

For which values of x does this equation stands true x² – 14x – 15 > 0 ?

A
x < –1

B
15 < x

C
–1 < x < 15

D
Both (a) and (b)

Solution

At x = 0 inequality is not satisfied.
Thus x = –1 and x = 15 are the roots of the quadratic equation.
Thus, option (d) is correct.
Question 3
3 / -1

For which values of x does this equation stands true |x² - 4x| < 5 ?

A
–1 < x < 5

B
1 ≤ x ≤ 5

C
–1 ≤ x ≤ 1

D
–1 ≤ x ≤ 5

Solution

At x = 0 inequality is satisfied, option(b) is rejected. At x = 2, inequality is satisfied, option (c) is rejected.
At x = 5, LHS = RHS.
At x = –1, LHS = RHS.
Thus, option (a) is correct.
Question 4
3 / -1

For which values of x does this equation stands true |x – 6| > x² – 5x + 9 ?

A
1 ≤ x < 3

B
1 < x< 3

C
2 < x < 5

D
–3 < x < 1
Solution
At x = 2, inequality is satisfied.
At x = 0, inequality is not satisfied.
At x = 1, inequality is not satisfied but LHS = RHS.
At x = 3, inequality is not satisfied but LHS = RHS.
Thus, option (b) is correct.
Question 5
3 / -1

For which values of x does this equation stands true |x² – 2x| < x ?

A
1 < x < 3

B
–1 < x < 3

C
0 < x < 4

D
x > 3
Solution
At x = 1 and x = 3
LHS = RHS.
At x = 2 inequality is satisfied.
At x = 0.1 inequality is not satisfied. At x = 2.9 inequality is satisfied.
At x = 3.1 inequality is not satisfied.
Thus, option (a) is correct.
Question 6
3 / -1

For which values of x does this equation stands true x² –7x + 12 < |x – 4| ?

A
x < 2

B
x > 4

C
2 < x < 3

D
2 < x < 4
Solution
At x = 0, inequality is not satisfied, option (a) is rejected.

At x = 5, inequality is not satisfied, option (b) is rejected.

At x = 2 inequality is not satisfied.

Thus, Option (d) is correct.
Question 7
3 / -1

For which values of x does this equation stands true |x² – 2x| < x ?

A
1 < x < 3

B
–1 < x < 2

C
0 < x < 4

D
–1 < x<0 , 0<x<3
Solution
At x = 1 and x = 3
LHS = RHS.

At x = 2 inequality is satisfied.

At x = 0.1 inequality is not satisfied. At x = 2.9 inequality is satisfied.

At x = 3.1 inequality is not satisfied. .

At x = 3, inequality is not satisfied but LHS = RHS.

Thus, option (d) is correct.
Question 8
3 / -1

For which values of x does this equation stands true 2 – x – x² ≥ 0 ?

A
–2 < x < 1

B
–2 ≤ x ≤ 1

C
x < –2

D
x > 1

Solution

At x = 0, inequality is satisfied.
Thus, options, (c) and (d) are rejected.

At x = 1, inequality is satisfied
Hence, we choose option (b).
Question 9
3 / -1

For which values of x does this equation stands true x² – |5x – 3| – x < 2 ?

A
x > 3 + 2√2

B
x < 3 +2√2

C
–5 < x < 3 + 2√2

D
x > – 5

Solution

At x = 0, inequality is satisfied, option (a) rejected. At x = 10, inequality is not satisfied, option (c) rejected.
At x = –5, LHS = RHS.
Also at x = 5, inequality is satisfied and at x = 6, inequality is not satisfied. Thus, option (c) is correct.
Question 10
3 / -1

For which values of x does this equation stands true |x² – 3x| + x – 2 < 0 ?

A
(1 – √3 , 2 – √2)

B
(1 - √3) < x < (2 + √2)

C
0 < x < 5

D
1 < x < 4

Solution

The options need to be converted to approximate values before you judge the answer. At x = 0, inequality is satisfied.
Thus, option (b) and (d) are rejected.
Option (a) is correct.

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Inequalities Test - 1

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Inequalities Test - 1

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SHARING IS CARING

Question 1

–2 < x < 2

x < – 0.66 or x > 3

3 < x < 7

–0.66 < x < 3 ​

Solution

Question 2

x < –1

15 < x

–1 < x < 15

Both (a) and (b) ​

Solution

Question 3

–1 < x < 5

1 ≤ x ≤ 5

–1 ≤ x ≤ 1

–1 ≤ x ≤ 5 ​

Solution

Question 4

1 ≤ x < 3

1 < x< 3

2 < x < 5

–3 < x < 1

Solution

Question 5

1 < x < 3

–1 < x < 3

0 < x < 4

x > 3

Solution

Question 6

x < 2

x > 4

2 < x < 3

2 < x < 4

Solution

Question 7

1 < x < 3

–1 < x < 2

0 < x < 4

–1 < x<0 , 0<x<3

Solution

Question 8

–2 < x < 1

–2 ≤ x ≤ 1

x < –2

x > 1

Solution

Question 9

x > 3 + 2√2

x < 3 +2√2

–5 < x < 3 + 2√2

x > – 5

Solution

Question 10

(1 – √3 , 2 – √2)

(1 - √3) < x < (2 + √2)

0 < x < 5

1 < x < 4

Solution

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–0.66 < x < 3

Both (a) and (b)

–1 ≤ x ≤ 5