Given A - x - 11 x -5-7 x -3- x - R and B - x - 18 x -9 - 15-12 x - x - R Find the range of set A - B-A- x- x - 4- x - RB- x - x - 4- x - R C- x - x 4- x - R

The correct option is A {x : x ≥ 4, x ϵ R}Let's take first inequation: 11x 5 gt; 7x + 3 Rule: If a term of an inequation is transferred from one side to ...

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Standard X

Mathematics

Solving Inequalities

Given A = x :...

Question

Given $A = {x : 11 x - 5 > 7 x + 3, x ϵ R}$ and $B = {x : 18 x - 9 \geq 15 + 12 x, x ϵ R} .$
Find the range of set $A \cap B$ .

{x : x \geq 4, x ϵ R}

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{x : x \leq 4, x ϵ R}

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{x : x < 4, x ϵ R}

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{x : x > 4, x ϵ R}

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Solution

The correct option is A ${x : x \geq 4, x ϵ R}$
Let's take first inequation:
$11 x - 5 > 7 x + 3$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

$\Rightarrow 11 x - 7 x > 5 + 3$

$\Rightarrow 4 x > 8$

$\Rightarrow x > 2$

$∴ A = {x : x > 2, x ϵ R}$ ...(i)
Let's take second inequation:

$18 x - 9 \geq 15 + 12 x$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

$\Rightarrow 18 x - 12 x \geq 15 + 9$

$\Rightarrow 18 x - 12 x \geq 24$

$\Rightarrow 6 x \geq 24$

$\Rightarrow x \geq 4$

$∴ B = {x : x \geq 4, x ϵ R}$ ...(ii)

The range of set $A \cap B = {x : x \geq 4, x ϵ R}$

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Similar questions

Given:

$A = {x : 11 x - 5 > 7 x + 3, x \in R}$ and

$B = {x : 18 x - 9 \geq 15 + 12 x, x \in R}$ .

Find the range of set $A \cap B$ .

Given
A = { $x : 11 x - 5 > 7 x + 3, x ϵ R$ }
B = { $x : 18 x - 9 \geq 15 + 12 x, x ϵ R$ }
Find the range of set $A \cap B .$

Q. Given
A = {

x : 11 x - 5 > 7 x + 3, x ϵ R

}
B = {

x : 18 x - 9 \geq 15 + 12 x, x ϵ R

}
The range of set

A \cap B

is .

Q. Given A =

x : 11 x - 5 > 7 x + 3, x ϵ R

and

B = x : 18 x - 9 \geq 15 + 12 x, x ϵ R .

Find the range of set

A \cap B

and represent it on a number line.
[3 MARKS]

Q. Let

A = {x : 11 x - 5 > 7 x + 3, x ϵ R}

and

B = {x : 18 x - 9 \geq 15 + 12 x, x ε R}

. Find the range of set

A \cap B

and represent it on the number line.
[4 MARKS]

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Given A={x:11x−5>7x+3,xϵR} and B={x:18x−9≥15+12x,xϵR}. Find the range of set A∩B.

Given $A = {x : 11 x - 5 > 7 x + 3, x ϵ R}$ and $B = {x : 18 x - 9 \geq 15 + 12 x, x ϵ R} .$
Find the range of set $A \cap B$ .