 Hello and welcome to the session. In this session we will discuss the following question and the question says solve the inequality 6 into x minus 3 the whole plus 4 is greater than 2 into 4x plus 7 the whole and graph its solution. Let's start the solution now. We are given this inequality and we have to solve it. So the given inequality is 6 into x minus 3 the whole plus 4 is greater than 2 into 3x plus 7 the whole. Now we will open the brackets. So this implies 6x minus 18 plus 4 is greater than 8x plus 14. This implies 6x minus 14 is greater than 8x plus 14. We will now add 14 to both sides. So this implies 6x minus 14 plus 14 is greater than 8x plus 14 plus 14. Since we have added same number to both sides so the sign of inequality remains the same. This implies 6x minus 14 and 14 get cancelled is greater than 8x plus 28. Now we subtract 8x from both sides. So this implies 6x minus 8x is greater than 8x plus 28 minus 8x. Since we have subtracted same number from both sides so the sign of inequality remains the same. This implies minus 2x is greater than 28 since 8x and minus 8x get cancelled. We now divide both sides by 2. So this implies minus x is greater than 28.2 that is 13. Now we multiply both sides by minus 1. So this implies x is less than minus 14. Since we have multiplied both sides by a negative number that is minus 1 so the sign of inequality changes. So this is the solution of the given inequality. We will now wrap the solution set on the number line. First we will make the number line. So this is the number line where the numbers to the right of 0 are all positive real numbers and the numbers to the left of 0 are all negative real numbers. We have to draw the graph where x is less than minus 14. Now this portion on the number line which is to the left of minus 14 contains values which are less than minus 14. Also minus 14 is not included in the solution set. So we draw an open circle at minus 14. Now we shade the portion to the left of minus 14 on the number line. The shaded portion contains values which are less than minus 14. We know that there exist infinitely many real numbers which are less than minus 14. So the shaded continues indefinitely to the left. So the shaded portion on the number line represents the graph of solution set. And this open circle at minus 14 means minus 14 is not included. With this we end our session. Hope you enjoyed the session.