Test: Inequalities - ACT MCQ

Amount left is at least 10 rupees i.e. amount left ≥ 10.
x - 40 ≥ 10 => x ≥ 50.

• Since it has highest power of x ‘2’ and has inequality sign so, it is called quadratic inequality.
• It is not numerical inequality as it does not have numbers on both sides of inequality.
• It does not have two inequality signs so it is not double inequality.

Since a variable ‘x’ is compared with number ‘5’ with inequality sign so it is called literal inequality.

Amount left is at most 10 rupees i.e. amount left ≤ 10.
x - 40 ≤ 10 => x ≤ 50.

Since it has equality sign along with inequality sign so it is a slack inequality not strict inequality.

• Since it has highest power of x ‘1’ and has inequality sign so, it is called linear inequality.
• It is not numerical inequality as it does not have numbers on both sides of inequality.
• It does not have two inequality signs so it is not double inequality.

Since here numbers are compared with inequality sign so, it is called numerical inequality.

Given 

x + 2y ≤ 3

x > 0 and y > 0

Calculation 

We need to satisfy the equation x + 2y ≤ 3 from the options 

Option: 1  x = -1 and y = 2 

This will be incorrect as we have x and y > 0 

In 1st option x is less than 0, so we can't take this 

Option: 2  x = 2, y = 1

2 + 2 ≤ 3 , which is incorrect.

Option: 3  x = 1, y = 1 

1 + 2 ≤  3 

3 ≤ 3, which is correct.

∴ The correct answer is x = 1, y = 1 

Given:

Initial ratio = 5 ∶ 6

Final ratio should be less than 17 ∶ 22

Calculation:

Let the least whole number that is needed to be subtracted be a.

According to the question,

(5 - a)/(6 - a) < 17/22

⇒ 5 × 22 - 22a < 17 × 6 - 17a 

⇒ 110 - 22a < 102 - 17a 

⇒ 110 - 102 < - 17a + 22a 

⇒ 8 < 5a 

⇒ 8/5 = 1.6 < a 

∴ The least whole number must be 2.

2x + 5 > 2 + 3x

5 – 2 > 3x – 2x

3 > x          .......(1)

2x - 3 ≤ 4x - 5

5 – 3 ≤ 4x – 2x

1 ≤ x          .......(2)

From (1) and (2)

x = 1 or 2