 Hello and welcome to the session. In this session we shall discuss how to evaluate expressions involving absolute value and variables for given values of the variables and how to apply geometric formulas in solving word problems. First of all let us discuss absolute value. Absolute value of our variable x is denoted by modulus of x. There are two ways to define absolute value and these are geometric definition and mathematical definition. Now we are going to discuss geometric definition. Absolute value of our variable x which is denoted by modulus of x is the distance of x from 0 on a number line. It is never negative as it measures distance not direction. This means absolute value of 4 is equal to 4 because 4 is 4 units to the right of 0 and absolute value of minus 4 is also equal to 4 because minus 4 is 4 units to the left of 0. We are now going to discuss mathematical definition. Absolute value of variable x is defined as now absolute value of variable x is equal to x if x is greater than or equal to 0 and absolute value of variable x is equal to minus x if x is less than 0. For example absolute value of 4 is equal to 4 because 4 is greater than 0 and absolute value of minus 4 is equal to minus of minus 4 which is equal to 4 because minus 4 is less than 0. Now we shall learn to evaluate expressions involving absolute value and variables for given value of the variables. Now steps for solving this type of equation involving absolute value and variables are as follows. Now the first step is to isolate the absolute value expression. Next we set the quantity inside the absolute value notation equal to plus and minus the quantity on the other side of the equation. Then we solve for the unknown variable in both equations and finally we check our answer. Now let us consider an example that is solve for x and the equation is absolute value of 3x minus 1 is equal to 4. Now we know that the first step involved in solving equation involving absolute value and variables is to isolate the absolute value expression and here we can see that the absolute value expression is already isolated. Then the next step is to set the quantity inside the absolute value notation equal to plus and minus the quantity on the other side of the equation. Now we have either 3x minus 1 is equal to 4 or 3x minus 1 is equal to minus 4 which implies that 3x is equal to 4 plus 1 or 3x is equal to minus 4 plus 1 which further implies that 3x is equal to 5 or 3x is equal to minus 3 which implies that x is equal to 5 by 3 or x is equal to minus 3 by 3 that is equal to minus 1. So we have got x is equal to 5 by 3 and x is equal to minus 1. Now these answers may not be the solutions to the equation. So let us check our answer by substituting x is equal to 5 by 3 and x is equal to minus 1 in the given equation. First of all we will put x is equal to 5 by 3 in the given equation and we get absolute value of 3 into 5 by 3 minus 1 is equal to 4 which implies that absolute value of 5 minus 1 is equal to 4 which further implies that absolute value of 4 is equal to 4 and we know that absolute value of 4 is equal to 4 which is equal to 4 and this is true. So x is equal to 5 by 3 is the solution of the given equation. Now we put x is equal to minus 1 in the given equation and we get absolute value of 3 into minus 1 minus 1 is equal to 4 which implies that absolute value of minus 3 minus 1 that is absolute value of minus 4 is equal to 4 and we know that absolute value of minus 4 is equal to 4 and that is equal to 4. So this is true. So x is equal to minus 1 is also the solution of the given equation. Thus we can say that x is equal to 5 by 3 and x is equal to minus 1 are the solutions of the given equation. Now we are going to discuss how to apply geometric formulas in solving word problems. In order to solve geometric word problems you will need to have memorized some geometric formulas for at least the basic shapes by this triangles, circles, squares, right triangles etc. Now the word problems can be solved by using these steps. The first step is reach the word problem carefully and write down what is to be found and what is given to us. Next we form an equation using a variable for the unknown quantity that is to be found and then we solve the equation to get the solution of the word problem. Let us consider an example. The length of the rectangular field is 2 times its breadth. If the area of the field is 15 meters square find its length and breadth. Now before solving this word problem we must know that area of rectangle is equal to length into breadth. Now here we are given that length of the rectangular field is 2 times its breadth. So now let breadth of the rectangle be equal to x so its length will be equal to 2 times breadth. Now here times is the keyword for multiplication so length will be equal to 2 into x that is equal to 2x. Now given area of rectangle is 50 meters square which implies that length into breadth will be equal to 50 meters square and here we know that length is 2 into x that is 2x into breadth that is x is equal to 50 meters square which further implies that 2x into x that is 2x square is equal to 50 meters square. This implies that x square is equal to 50 by 2 meters square that is equal to 25 meters square which implies that x is equal to square root of 25 meters square which implies that x is equal to now here taking positive square root we get 5 meters so breadth which is equal to x is equal to 5 meters and length which is equal to 2 into x that is 2x is equal to 2 into 5 that is equal to 10 meters so we can say that length and breadth of the rectangular field are 10 meters and 5 meters respectively. Thus in this session we have discussed how to evaluate expressions involving absolute value and variables for given values of the variables and how to apply geometric formulas in solving word problems. This completes our session hope you enjoyed this session.