 Hello and welcome to the session. In this session we will discuss a question which says that written in the range of values for which 3 minus 2x square is greater than 5x. Now before starting the solution of this question, we should know about a method. And this is the method of intervals. For this method, the first step is to factorize the quadratic expression whose coefficient of x square is positive and express the left hand side to the inequality in the form x minus alpha the whole into x minus beta the whole where alpha is less than beta. Now in the next step, plot the points alpha and beta on the number line thus dividing the number line into 3 parts. Now after plotting the points alpha beta on the number line starting from the right most region, put the signs plus, minus and plus which shows that the expression x minus alpha the whole into x minus beta the whole is non-negative in the region on the right to beta. Now when x minus alpha into x minus beta the whole is less than 0 then the required range will be alpha less than x less than beta. Now this method will work out as a key idea for solving out this question. And now we will start with the solution. Here it is given 3 minus 2x square is greater than 5x. This implies minus 2x square minus 5x plus 3 is greater than 0. Now multiplying both sides by minus 1. This implies 2x square plus 5x minus 3 is less than 0. On multiplying by a negative quantity the inequality reverses. Now this implies factorizing this by splitting the middle term it will be 2x square plus 6x minus x minus 3 is less than 0. This implies 2x within brackets x plus 3 here minus 1 is common and within brackets x plus 3 is less than 0. This implies x plus 3 the whole into 2x minus 1 the whole is less than 0. Now putting each factor equal to 0 we get x is equal to minus 3 and 1 by 2. Now here plotting these points on the number line and by using the method of intervals. So we have plotted the points minus 3 and 1 by 2 on the number line and starting from the right we have given the sign plus minus and plus. As plus 3 the whole into 2x minus 1 the whole is less than 0. Therefore the required range will be according to the formula given in the key idea. If x minus alpha the whole into x minus beta the whole is less than 0. Then the required range is alpha less than x less than beta. So the required range will be minus 3 less than x less than 1 by 2. So this is the solution of the given question and that's all for the session. Hope you all have enjoyed the session.