Question
Isabel says that the equation x-2= -(x-2) has no solution because a number can never be equal to its opposite, Explain the error Isabel made .
Hint:
An equation with variables on both sides of the "equal to" sign i.e. on LHS and RHS can be solved by first simplifying both the sides (Opening up the brackets, addition, subtraction, i.e. if any) and then all the variables are taken on 1 side of the equation and all the constants i.e. numbers on the other side. Both sides are then simplified further and the solution is obtained
The correct answer is: Hence, Isabel's error is that she did not consider a possibility of getting a value of x for which the final solution could be 0 for the given system of equations.
Step-by-step solution:-
We will solve the given equation and check whether solution exists for the same or not-
x - 2 = -(x - 2)
∴ x - 2 = -x - (-2) …..................................... [Distributive property- a (m + n) = am + an]
∴ x - 2 = -x + 2
∴ x + x = 2 + 2 ........................................... (Taking all variables and constants together)
∴ 2x = 4
∴ x = 4/2 ............................................. (Dividing both sides by 2)
∴ x = 2
Hence, Isabel's conclusion on the given equation having no solution is incorrect.
Reason-
LHS = x - 2 = 2 - 2 = 0
RHS = - (x - 2) = - (2 - 2) = - (0) = 0
When we substitute x = 2 in the given equation, we see that-
LHS = RHS = 0 and we know that 0 is the only number that is equal to its opposite (as -0 doesn't exist).
Hence, Isabel's error is that she did not consider a possibility of getting a value of x for which the final solution could be 0 for the given system of equations.
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