Question

How do you solve \[7 - 5x = - 5x - 6x + 7?\]

Answer 1

Hint: Try to group similar terms together, grouping is done by keeping all the constant terms on one side and all the variable terms on the other side.\[ \Rightarrow - 5x + 5x + 6x = 7 - 7\]


Complete step by step answer:
The given equation is \[7 - 5x = - 5x - 6x + 7\]
We observe that all the terms are not in their correct form.
We need to group similar terms together in order to further simplify the equation.
Bring all the variable terms on one side and all the constant terms on one side. This is the standard way of grouping terms.
Grouping the similar terms, adding and subtracting similar terms we get
\[ \Rightarrow 0 + 6x = 0\]
By adding the terms, we get
\[ \Rightarrow 6x = 0\]
Dividing by on both the sides of the equation by $6$
\[ \Rightarrow \dfrac{x}{6} \times 6 = \dfrac{0}{6}\]
On simplifying, we get
\[ \Rightarrow x = 0\]

Therefore, the simplified form of the given equation is \[x = 0\]

Note: One should always remember that if a positive term is shifted from one side of the equation to the other side, it becomes negative and vice versa. Also, the equation does not affect or change if the same quantity is added, subtracted, multiplied or divided with the terms on both sides of the equation. Hence, in this case, we divided both side by \[6\]
One should remember that zero divided by any number other than zero will return a value of zero only. Never divide zero by zero as the value then returned is not defined. It is preferred to shift the negative sign to the other side of the equation by multiplying both sides with a negative sign. Again, multiplication does not change the equation, and the negative multiplied with negative gives a positive on the desired side of the equation.