Let T - x - x -5- x -7-5-4 x -40-13- x - Is T an empty set - Justify your answer-

Since, {x|x+5/x 7 5 = 4x 40/13 x} x+5/x 7 5=4x 40/13 x ⇒x+5 5(x 7)/x 7=4x 40/13 x ⇒x+5 5x+35/x 7=4x 40/13 x ⇒ 4x+40/x 7=4x 40/13 x ⇒ (4x+40)(13 x)=(4x 4 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Properties of Inequalities

Let T = x | x...

Question

Let T = ${x | \frac{x + 5}{x - 7} - 5 = \frac{4 x - 40}{13 - x}}$ . Is T an empty set ? Justify your answer.

Open in App

Solution

Since, ${x | \frac{x + 5}{x - 7} - 5 = \frac{4 x - 40}{13 - x}} \frac{x + 5}{x - 7} - 5 = \frac{4 x - 40}{13 - x} \Rightarrow \frac{x + 5 - 5 (x - 7)}{x - 7} = \frac{4 x - 40}{13 - x} \Rightarrow \frac{x + 5 - 5 x + 35}{x - 7} = \frac{4 x - 40}{13 - x} \Rightarrow \frac{- 4 x + 40}{x - 7} = \frac{4 x - 40}{13 - x} \Rightarrow - (4 x + 40) (13 - x) = (4 x - 40) (x - 7) \Rightarrow (4 x - 40) (x - 7) + (4 x - 40) (13 - x) = 0 \Rightarrow (4 x - 40) (x - 7 + 13 - x) = 0 \Rightarrow 24 (x - 10) = 0 \Rightarrow x = 10 ∵ T = {10}$

Hence, T is not an empty set.

Suggest Corrections

Similar questions

Q. Given a non empty set X, consider

P (X)

which is set of all subsets of

X

. Define the relation

R

P (X)

as follows:
For subsets

A, B

P (X), A R B

if and only if

A \subset B

. Is R an equivalence relation on

P (X)

? Justify your answer

Q. Give a non-empty set

X

. Consider

P (X)

, which is the set of all subsets of

X

. Define the relation

R

P (X)

as follows:
For subsets

A

and

B

P (X)

A R B

A \subset B

, is

R

an equivalence relation on

P (X)

?
Justify your answer.

Given a non-empty set X. Consider P(X), which is the set of all subset of X. Defined the relation R in P(X) as follows:
For subsets A and B in P(X),ARB if and only if $A \subset B$ . Is R an equivalence relation on P(X)? Justify your answer.

Q. Do the equations 5x+7y=8 and 10x+14y=4 represent a pair of concident lines ? Justify your answer.

Q. Classify the following set as 'singleton' or 'empty':

C = {x | x

is natural number,

5 < x < 7}

Join BYJU'S Learning Program

Let T = {x|x+5x−7−5=4x−4013−x}. Is T an empty set ? Justify your answer.

Let T = ${x | \frac{x + 5}{x - 7} - 5 = \frac{4 x - 40}{13 - x}}$ . Is T an empty set ? Justify your answer.