Question

How do you solve \[ - 5x - 7 = - 3x + 1?\]

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.

Complete Step by Step Solution:
The given equation is \[ - 5x - 7 = - 3x + 1\]
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 the other side. This is the standard way of grouping terms.
\[ \Rightarrow - 5x + 3x = 7 + 1\]
Grouping the similar terms, adding and subtracting similar terms we get
\[ \Rightarrow - 2x = 8\]
Dividing by on both the sides of the equation by \[ - 2\] we get,
\[ \Rightarrow \dfrac{{ - 2x}}{{ - 2}} = \dfrac{8}{{ - 2}}\]
We just cancel out the numbers from the numerator and denominator
\[ \Rightarrow x = - 4\]

Therefore, the simplified form of the given equation is x = - 4

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.
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 $ - 2.$
One has to know that while writing the answers, it is convenient to not write the final value of the variable as \[ - x = 8\] .
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.