Question

A={x:4<3x-2 <= 13 ,x= R}
B = { x:-2<=5+7x<40,x=R}
Write down the elements
Draw the number line A & B.​

Answer 1

Answer:

A={3,4,5}

B={1,2,3,4} is the correct answer

Answer 2

Therefore the number line is drawn successfully for 'A' and 'B'.

Given:

Set of numbers in A = { x : 4 < 3x - 2 ≤ 13, x = R }

Set of numbers in B = { x : -2 ≤ 5 + 7x < 40, x = R }

To Find:

A number line should be drawn for 'A' and 'B'.

Solution:

The number line for the given question can be drawn very easily as shown below.

Given that,

Set of numbers in A = { x : 4 < 3x - 2 ≤ 13, x = R }

Set of numbers in B = { x : -2 ≤ 5 + 7x < 40, x = R }

Consider set 'A':

Condition: x : 4 < 3x - 2 ≤ 13, x = R

Lower limit: 4 < 3x - 2 ⇒ 4 + 2 < 3x ⇒ 6 < 3x ⇒ x > 2

Higher limit: 3x - 2 ≤ 13 ⇒ 3x ≤ 13 + 2 ⇒ 3x ≤ 15 ⇒ x ≤ 5

So after solving the inequalities 'A' can be written as shown below,

⇒ A = { x : 2 < x ≤ 5, x ∈ R } = { 3, 4, 5 }

Set of numbers in B = { x : -2 ≤ 5 + 7x < 40, x = R }

Consider set 'B':

Condition: x : -2 ≤ 5 + 7x < 40 , x ∈ R

Lower limit: -2 ≤ 5 + 7x ⇒ -2 -5 ≤ 7x ⇒ -7 ≤ 7x ⇒ x ≥ -1

Higher limit: 5 + 7x < 40 ⇒ 7x < 40 - 5 ⇒ 7x < 35 ⇒ x < 5

So after solving the inequalities 'B' can be written as shown below,

⇒ B = { x : -1 ≤ x < 5, x ∈ R } = { -1, 0, 1, 2, 3, 4 }

Therefore the number line is drawn successfully for 'A' and 'B'.

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