 Hello and welcome to the session. In this session, we will discuss a question that says that which of the following linear equations has one solution, no solution or infinitely many solutions? First pattern, 7 into n minus 3 the whole is equal to 7. Second pattern, 2 upon 3 into x minus 4 is equal to 2 into 1 upon 3 into x minus 2 the whole. And third pattern, 4x plus 5 is equal to 2 into 2x plus 5 the whole. Now before starting the solution of this question, we should know some results. First is if two expressions remain equivalent for any value of variable, then it has infinitely many solutions. And the second result is if two expressions are not equivalent for every value of variable, then it has no solution. And the third result is only one value of variable satisfies the equation, then it has one solution. Now these results will welcome to the key idea for solving the given question. Now let us start with the solution of the given question. Now let us start with the first part. Now in the first part equation is given to us as 7 into n minus 3 the whole is equal to 7. Now let us solve this equation. Now this implies 7 into n minus 7 into 3 which is 21 is equal to 7. And this implies 7 into n is equal to 7 plus 21 and this gets 7 into n is equal to 28 which further implies n is equal to 28 upon 7 which is equal to 4. Therefore n is equal to 4. Now let this equation be equation number one. Now on solving this equation we have obtained m is equal to 4. Now the only learning of m that means equation one true. That means for m is equal to 4 the left hand side will be equal to the right hand side of this equation. Let us verify this. Now putting is equal to 4 in equation one we get 7 into 4 minus 3 the whole is equal to 7. And this implies 7 into now 4 minus 3 is 1 and 7 into 1 is 7 and this is equal to left hand side is equal to right hand side. Hence this equation is satisfied for m is equal to 4. Now if we put any other value of variable m then left hand side will not be equal to right hand side of this equation m is equal to 1. In equation one then we have 7 into 1 minus 3 the whole is equal to 7 which implies 7 into now 1 minus 3 is minus 2. Is equal to 7 and this implies minus 14 is equal to 7 and this is not minus 14 is not equal to 7. Similarly you can take any other value of the variable m but no value will satisfy the equation one except m is equal to 4. And from the key idea we know that if only one value of variable satisfies the equation then it has one solution. So the given equation has one solution that is m is equal to 4. Now let us start with the second part. In the second part the equation is given to us as 2 upon 3 into x minus 2 into 1 upon 3 into x minus this equation. Now this implies 2 upon 3 into x minus 4 is equal to now using the distributive property this will be 2 into 1 upon 3 into x minus 2 into 2 and 3 into x minus 4 is equal to 2 upon 3 into x minus now 2 into 2 is. Now subtracting into x from both sides we get minus 4 is equal to minus 4. So it appears 4 is equal to 4. Any real value left inside is equal to right inside for every value of the variable m it means these two expressions remain equivalent for every value of variable when it has infinite many solutions. So here the given equation has many solutions. Now let us start with third part. Now in the third part the equation is equal to 2 into 2 into x. Let us simplify this equation. Now this implies 4 x plus 5 equal to now using the distributive property this is equal to 2 into 2 x plus 2 into 5. 4 x plus 5 is equal to now 2 into 2 x is equal to 4 x. Now subtracting 4 x from both sides we get 5 is equal to 10 which is not possible not equal to 10. So here is not equal to right inside for any value of x this means these two expressions are not equivalent for every value of the variable x. Now from the key idea we know that if two expressions are not equivalent for every value of the variable that it has no solution. So here the given equation has no solution and this completes our session. Hope you all have enjoyed the session.