Question

Find the solution set and represent the same on the number line

1 ≤ 3(x – 2) + 4 < 7 , x ∈ W.​

Answer 1

Answer :

• The solution set of 1 ≤ 3(x – 2) + 4 < 7 , x ∈ W is { 1, 2, 3 }
• Number line = Refer the attached.

Step-by-step explanation ::

To Find :-

• The solution set of the linear inequation
• Represent the it one number line

Solution :-

Given that,

1 ≤ 3(x – 2) + 4 < 7 , x ∈ W

According the question,

The solution set is,

Case 1: 1 ⩽ 3( x - 2 ) + 4

⟹ 1 ⩽ 3( x - 2 ) + 4

⟹ 1 ⩽ 3x - 6 + 4

⟹ 1 ⩽ 3x - 2

⟹ 1 + 2 ⩽ 3x

⟹ 3 ⩽ 3x

⟹ 3/3 ⩽ x

⟹ 1 ⩽ x

Case 2: 3( x - 2 ) + 4 < 7

⟹ 3( x - 2 ) + 4 < 7

⟹ 3x - 6 + 4 < 7

⟹ 3x - 2 < 7

⟹ 3x < 7 + 2

⟹ 3x < 9

⟹ x < 9/3

⟹ x < 3

Therefore, the solution set is { 1, 2, 3 }.

Now, the number line ::

• Refer the attachment.