 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve two given equations for x and the equation is absolute value of x minus 1 the whole plus 6 is equal to 2x plus 3. We know that the steps for solving the equation involving absolute value and variables are as follows. The first step is isolate the absolute value expression then set the quantity inside the absolute value notation equal to plus and minus the quantity on the other side of the equation. Then solve for the unknown variable in both equations and check your answer. With this key idea we shall proceed to the solution. Here we are given the equation absolute value of x minus 1 the whole plus 6 is equal to 2x plus 3. Now using these steps given in the key idea here we first isolate the absolute value expression and we get absolute value of x minus 1 the whole is equal to 2x plus 3 minus 6 which implies that absolute value of x minus 1 the whole is equal to 2x minus 3. In the next step we set the quantity inside the absolute value notation equal to plus and minus the quantity on the other side of the equation. So now either x minus 1 is equal to 2x minus 3 or x minus 1 is equal to minus of 2x minus 3 the whole. Then in the next step we solve for the unknown variable in both equations and here we have either x minus 1 is equal to 2x minus 3 or x minus 1 is equal to minus of 2x minus 3 the whole which implies that x minus 2x is equal to minus 3 plus 1 or x minus 1 is equal to minus 2x plus 3 this further implies that minus x is equal to minus 2 or x plus 2x is equal to 3 plus 1 this further implies that x is equal to 2 or 3x is equal to 4 that is x is equal to 2 or x is equal to 4 by 3 now we have got two values for x these answers will not be the solutions to the equation so in the last step we check our answers first two phone we shall put x is equal to 2 in the given equation and we get absolute value of 2 minus 1 the whole plus 6 is equal to 2 into 2 plus 3 which implies that absolute value of 1 plus 6 is equal to 4 plus 3 which further implies that now absolute value of 1 is 1 plus 6 is equal to 4 plus 3 that is 7 which implies that 7 is equal to 7 which is true so x is equal to 2 satisfies the given equation hence it is the solution of the given equation now we put x is equal to 4 by 3 in the given equation and we get absolute value of 4 by 3 minus 1 the whole plus 6 is equal to 2 into 4 by 3 plus 3 which implies that absolute value of 4 minus 3 by 3 the whole plus 6 is equal to 2 into 4 by 3 plus 3 this further implies that absolute value of 1 by 3 plus 6 is equal to 8 by 3 plus 3 that is now absolute value of 1 by 3 is equal to 1 by 3 so we have 1 by 3 plus 6 is equal to now taking LCM here we get 8 plus 9 upon 3 that is 17 by 3 this further implies that 1 plus 18 whole upon 3 is equal to 17 by 3 which implies that 19 by 3 is equal to 17 by 3 which is not true so x is equal to 4 by 3 does not satisfy the given equation hence it is not the solution of the given equation thus we can say that x is equal to 2 is the solution of the given equation that is absolute value of x minus 1 the whole plus 6 is equal to 2x plus 3 this is the required answer this completes our session hope you enjoyed this session