 Hi and how are you all today? I am Priyanka and let us discuss the following question. It says solve the inequalities for real x. So in this question we need to find the value of x, let us find it out. The inequality given to us is 1 by 2, 3x divided by 5 plus 4 is greater than equal to 1 by 3 x minus getting multiplied by x minus 6. Now here first of all on removing the brackets we have 3x divided by 10 plus 2 is greater than equal to x by 3 minus 2. Now on multiplying both the sides by 30 that is the LCM of 10 and 3 we have 9x plus 60 is greater than equal to 10x minus 60. On subtracting 60 from both the sides we have 9x plus 60 minus 60 is greater than equal to 10x minus 60 minus 60. After simplification we have 9x is greater than equal to 10x minus 120. Now on subtracting 10x from both the sides we have 9x minus 10x is greater than equal to 10x minus 120 minus 10x. After simplification we have minus x is greater than equal to minus 120. Now on multiplying both the sides by a negative number that is minus 1 we have a reversed sign of inequality in between now. On solving it we have x is less than equal to 120. So for real x the solution set consists of all real numbers which are less than equal to 120. So an open interval from one side and a closed interval from the other side of 120 is also equal to x hence it will be included in the interval. So I hope you can solve more of these types by for now.