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Solve the following inequations. 

(i) x < 7, where x is a natural number. 

(ii) x – 6 < 1, where x is a natural number.

(iii) 2a + 3 < 13, where a is a whole number. 

(iv) 6x – 7 > 35, where x is an integer. 

(v) 4x – 9 > -33, where x is a negative integer.

1 Answer

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(i) x < 7, where x is a natural number. 

Since the solution belongs to the set of natural numbers, that are less than or equal to 7, we take the values of x as 1,2, 3, 4, 5, 6 and 7.

(ii) x – 6 < 1, where x is a natural number. 

x – 6 < 1 Adding 6 on the both the sides x – 6 + 6 < 1 + 6 

x < 7 

Since the solutions belongs to the set of natural numbers that are less than 7, we take the values of x as 1,2, 3, 4, 5 and 6

(iii) 2a + 3 < 13, where a is a whole number. 

2a + 3 < 13 

Subtracting 3 from both the sides 2a + 3 – 3 < 13 – 3 

2a < 10 

Dividing both the side by 2. \(\frac{2a}{2}\) < a \(\frac{10}{2}\)

a <

Since the solutions belongs to the set of whole numbers that are less than or equal to 5 we take the values of a as 0, 1, 2, 3, 4 and 5.

(iv) 6x – 7 > 35, where x is an integer. 

6x – 7 > 35 Adding 7 on both the sides 

6x – 7 + 7 > 35 + 7

6x > 42

Dividing both the sides by 6 we get \(\frac{6x}{6}\) > \(\frac{42}{6}\)

x >

Since the solution belongs to the set of integers that are greater than or equal to 7, we take the values of x as 7, 8, 9, 10…

(v) 4x – 9 > -33, where x is a negative integer. 

4x – 9 > – 33 + 9 

Adding 9 both the sides 4x – 9 + 9 > -33 + 9 

4x > – 24 

Dividing both the sides by 4

\(\frac{4x}{4}\) > \(\frac{-24}{4}\) 

x > -6 

Since the solution belongs to a negative integer that are greater than -6, we take values of u as -5, -4, -3, -2 and -1.

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