 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says solve the following inequalities and represent the solution graphically on number 9. Eighth question is 2 into x minus 1 is strictly less than x plus 5. 3 into x plus 2 is strictly greater than 2 minus x. In this question first we have to solve the given inequalities and then we have to represent the solution graphically on the number line. Now let us start with the solution square. Here the two inequalities given to us are 2 into x minus 1 strictly less than x plus 5 and second inequality is 3 into x plus 2 is strictly greater than 2 minus x. Now we consider the first one. First inequality is 2 into x minus 1 is strictly less than x plus 5 or we can say 2x minus 2 is strictly less than x plus 5 or 2x is strictly less than x plus 7 or x is strictly less than 7. Now the second inequality is 3 into x plus 2 is strictly greater than 2 minus x or 3x plus 6 is strictly greater than 2 minus x or 3x is strictly greater than minus 4 minus x or 4x is strictly greater than minus 4 or x is strictly greater than minus 1. Hence the values of x satisfying the both inequalities are given by x lies between minus 1 and 7 where minus 1 and 7 are not included. Now we can say that the solution set is minus 1, 7 where minus 1 and 7 are not included. So this is our answer to this question. Now we see the graphic presenting of the solution set on the number line. Now this is the number line and the required solution set is minus 1 to 7 that is this line. But here we also see that minus 1 and 7 are not included. So this is our answer to this question. I hope you understood the question and enjoyed the session. Have a good day.