Question

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-2 +10x<=13x+10<24+10x, x∈Z.

Solve the following inequation, write down the solution set and represent it on the real number line.

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Answer 1

Answer :-

• Solution set = { x ∈ Z : -4 ⩽ x < 14/3 }
• Number line = Refer the attachment.

Step-by-step explanation :-

To Find :-

• The solution set
• Represent it on real number line

Solution:

Case 1 :-

• -2 + 10x ⩽ 13x + 10

⟹ -2 + 10x ⩽ 13x + 10

Transposing 13x to L.H.S,

⟹ -2 + 10x - 13x ⩽ 10

Transposing -2 to R.H.S,

⟹ 10x - 13x ⩽ 10 + 2

⟹ -3x ⩽ 10 + 2

⟹ -3x ⩽ 12

Transposing -3 to R.H.S,

⟹ x ⩾ -12/3

⟹ x ⩾ -4

Case 2 :-

• 13x + 10 < 24 + 10x

⟹ 13x + 10 < 24 + 10x

Transposing 10 to R.H.S,

⟹ 13x < 24 - 10 + 10x

Transposing 10x to L.H.S,

⟹ 13x - 10x < 24 - 10

⟹ 3x < 24 - 10

⟹ 3x < 14

Transposing 3 to R.H.S,

⟹ x < 14/3

According the question,

• The solution set is,

Solution set ( whole inequation )

⟹ { x ∈ Z : -4 ⩽ x < 14/3 }

Now,

• Real number line

Refer the attachment.